Building-block package

Scale V4.1

Maximum-rigor all-gate Scale building blocks for tracking transformations, dimensions, anomalies, critical behavior, regional composition, and the evidence needed to evaluate every gate without promoting unsupported claims.

Complete package browser · 99 files · source archive: scale.zip

Validation status: PASS. The package reports 26/26 constraints, 30/30 gates, 35/35 packet schemas, and zero validation errors. Its canonical authority is 01_CORE/BB_SCL_4_1_MAX_RIGOR_ALL_GATE_SCALE.md; earlier Scale sources are preserved for comparison.

Use the single-column folder list below to open any source file. The canonical authority, README, and Start Here files are expanded first.

01_CORE
- BB_SCL_4_1_MAX_RIGOR_ALL_GATE_SCALE.md
02_REGISTRIES
03_EXECUTION
04_VALIDATION
05_REGRESSION
06_SOURCES
07_SCRIPTS
08_TEMPLATES
- EMPTY_SCALE_PACKET_BUNDLE.json
- GATE_SCALE_WORKSHEET.md
README.md
- README.md
START_HERE.md
- START_HERE.md

How to use this package

Start with START_HERE.md and the canonical Scale authority. Load the gate crosswalk, instantiate all 35 packet types, execute active packets, record inactive packets as typed NOT-APPLICABLE, and run the validator and controls. Missing evidence remains OPEN; this package does not certify candidate-specific gate evidence.

01_CORE

Canonical authority and the complete Granularity rulebook.

BB_SCL_4_1_MAX_RIGOR_ALL_GATE_SCALE.md1,20,442 bytes

scale/01_CORE/BB_SCL_4_1_MAX_RIGOR_ALL_GATE_SCALE.md

--- title: "BB-SCL-4.1 — Maximum-Rigor All-Gate Scale Authority" buildingblockid: "BB-SCL-4.1" version: "4.1" date: "2026-08-02" status: "DEVELOPMENT AUTHORITY — MAXIMUM-RIGOR — NOT CANONICALLY RATIFIED" supersedesfordevelopment: "BB-SCL-4.0 and BB-SCL-3.3 while preserving both exactly" ---

BB-SCL-4.1 — Maximum-Rigor All-Gate Scale Authority

0. Governing question

Scale answers:

How do structural relations, states, dynamics, boundaries, observers, and refinements acquire comparable physical magnitudes—without hiding inputs, fluctuations, scheme dependence, uncertainty, thresholds, towers, or vacuum terms?

Scale is not merely “the list of numbers.” It is the typed system that assigns provenance, units, frames, normalization, matching, uncertainty, and validity domains to every magnitude and coefficient used by the theory.

The controlling anti-substitution firewalls are:

eq$ associated fluctuation absent$;

eq$ radion stabilized$;

eq$ vacuum value prediction$;

eq$ unowned$;

eq$ radiative stability$;

eq$ all-scale completion$;

eq$ same ruler$;

eq$ independent prediction$;

eq$ protected hierarchy$;

eq$ state-independent physical scale$;

$background value fixed $
$measured radius $
$vacuum stability $
$dimensionless $
$one-scale cancellation $
$finite tower $
$same symbol $
$calibrated datum $
$small number $
$fixed coordinate scale $

1. Authority precedence and preservation

BB-SCL-4.1 is the controlling development authority for Scale when explicitly selected.
Every normative datum, schema, firewall, control, and acceptance rule in BB-SCL-4.0 and BB-SCL-3.3 remains binding unless BB-SCL-4.1 explicitly strengthens it.
The exact BB-SCL-3.3 source is archived in 06SOURCES/BBSCL33EXACTARCHIVAL_SOURCE.md; its SHA-256 is recorded in the preservation matrix.
Existing gate terminals are not inherited as evidence. They are source claims to be rerun under current authority hashes.
In a conflict, the stricter claim ceiling and the more explicit physical/evidence distinction govern until adjudicated.

2. Ownership and non-ownership

2.1 Scale owns

provenance and unique ownership of magnitudes and coefficients;
dimensional, unit, frame, and normalization closure;
same-ruler comparison and transport;
anchor identifiability and absolute-unit requirements;
background-scale versus fluctuation ledgers;
quantitative gaps, cutoffs, observation windows, and decoupling margins;
multiplier/stiffness classification;
equal parameter and discrete-choice accounting;
vacuum-term scale/provenance decomposition;
stability-versus-value ownership;
threshold, phase-transition, and history scale ledgers;
renormalization, scheme, RG, and matching transport;
measured/calibrated/predicted role separation;
topological and inflow coefficient normalization and quantization;
uncertainty covariance, sensitivity, and identifiability;
hierarchy and radiative-sensitivity diagnosis;
multi-scale EFT/tower/tail scope;
state-, region-, temperature-, horizon-, and clock-dependent scales;
composite/emergent/effective scale provenance;
resolution/refinement lattice consistency;
scale grammar saturation and exhaustion;
scale-transformation covariance, homogeneity, and anomalous dimensions;
scale-symmetry breaking, trace/Weyl anomaly, and dimensional transmutation;
criticality, universality, finite-size scaling, and crossover;
extensive/intensive, area/volume/fractal scaling, and regional composition;
non-gating economy vectors;

2.2 Scale does not independently own

which supports or Actors exist (Shape);
the parent equations that generate masses, histories, and rates (Dynamics);
operator domains and inflow consistency (Boundary);
candidate equivalence and test-family saturation (Granularity);
modulus stability (Rigidity);
vacuum-offset response law and cosmological solution (Vacuum);
the actual parent-to-record map (Observer);
clock synchronization and causal order (Time Synchronization);
status generation and closure governance (CSE/Constitution);

Scale consumes typed certificates from these blocks and refuses to promote their missing evidence into a Scale PASS.

3. Complete Scale object

For a frozen branch $\mathfrak P$, define \[ \mathfrak S{\rm scale}= (\mathcal U{\rm scl},\operatorname{prov},\operatorname{owner},\dim,F,N,\mathfrak R, \mathcal A,\mathcal G,\mathcal P,\mathcal V,\mathcal T,\mathcal C,\Sigma,\mathcal L,\mathcal W,\mathcal A{\rm sc},\mathcal K,\mathcal X), \] where $\mathcal U{\rm scl}$ is the generated scale-object roster; $\dim,F,N$ are dimension, frame, and normalization maps; $\mathfrak R$ is the ruler tuple; $\mathcal A$ anchors; $\mathcal G$ gaps; $\mathcal P$ parameter ledger; $\mathcal V$ vacuum ledger; $\mathcal T$ threshold/history ledger; $\mathcal C$ coefficient-quantization ledger; $\Sigma$ covariance/sensitivity data; and $\mathcal L$ the resolution/refinement lattice; $\mathcal W$ the scale-transformation representation; $\mathcal A_{\rm sc}$ the scale-anomaly/transmutation ledger; $\mathcal K$ the critical/universality data; and $\mathcal X$ the regional composition/scaling law.

A gate-scale certificate is admissible only if every applicable component is populated or explicitly OPEN/NOT-APPLICABLE with a type proof.

4. Provenance classes

Every scale object receives exactly one primary class:

MEASURED-ANCHOR;
CALIBRATION-INPUT;
DERIVED-GIVEN-ANCHOR;
THEOREM-DERIVED;
STRUCTURAL-NORMALIZATION;
CONSTRAINT-MULTIPLIER;
PHYSICAL-COUPLING;
GLOBAL-INTEGRATION-CONSTANT;
BOUNDARY-DATUM;
MATCHING-OUTPUT;
SCHEME-DEPENDENT-INTERMEDIATE;
MEASURED-RESIDUAL;
BLIND-PREDICTION;
DERIVED-STATE-DEPENDENT;
DERIVED-EMERGENT;
FORBIDDEN-UNDECLARED;

Secondary tags may record dependencies, but primary provenance is unique and frozen before outcome inspection.

5. Same-ruler contract

Every comparison freezes \[ \mathfrak R=(D{\rm parent},D{\rm observer},\text{frame},\mu,\text{scheme}, N{\rm bundle},N{\rm field},G{\rm global},\Pi,\Lambda{\rm cutoff}, \Delta_{\rm resolution},\text{truncation},\text{regulator},\text{observable definition},\text{time standard}). \] A hash mismatch suspends comparison unless the complete transport and covariance are supplied.

6. Constraint system

SCL-C01 — Universal scale provenance and unique ownership

Question. Does every magnitude, coefficient, cutoff, tolerance, normalization, discrete scale choice, and residual have exactly one frozen provenance class and one primary owner?

For the scale-object universe $\mathcal U{\rm scl}$, require a total typed map \[ \operatorname{prov}:\mathcal U{\rm scl}\rightarrow\mathcal P{\rm allowed}, \qquad \operatorname{owner}:\mathcal U{\rm scl}\rightarrow\mathcal B, \] with exactly one primary value for each map. Provenance may be refined by secondary dependencies but may not be changed after a gate result is inspected.

Required inputs

all numerical and discrete objects;
parent-term ledger;
calibration and measurement manifest;
gate freeze hash;

Execution algorithm

enumerate every load-bearing scalar, tensor coefficient, scale and tolerance.
assign one allowed provenance class.
assign one primary block/parent-term owner.
run duplicate, orphan, and post-target mutation tests.

Required outputs

provenance_ledger;
dependency_hashes;

Minimal discharge. Complete machine-readable provenance table with zero orphan, duplicate-primary, or post-freeze mutation rows.

Fail trigger. Any load-bearing quantity is unowned, multiply primary-owned, retrospectively reclassified, or supplied only by the desired gate result.

Destructive control. Insert a dimensionless coefficient with no owner; the validator must fail.

SCL-C02 — Dimensional, unit, frame, and normalization closure

Question. Are every equation and comparison dimensionally closed in one declared frame and normalization system?

Every asserted equality $X=Y$ requires \[ [ X ]=[ Y ],\quad FX=FY,\quad NX=NY, \] where $[\cdot]$ is the unit/dimension vector, $F$ the physical frame, and $N$ the complete field, trace, bundle, quotient, and measure normalization packet.

Required inputs

equation vector;
unit basis;
frame map;
normalization ledgers;

Execution algorithm

construct dimension vectors for every term.
transport all terms to a frozen frame.
apply trace/bundle/field/quotient normalization maps.
reject unmatched or implicit conversion factors.

Required outputs

dimensionalclosurepacket;
samerulerpacket;

Minimal discharge. Symbolic dimensional audit plus explicit frame and normalization transforms for every compared quantity.

Fail trigger. An equality, inequality, gap, anomaly coefficient, or residual is compared across inconsistent units, frames, or normalizations.

Destructive control. Compare a 13D coefficient directly to a 4D canonically normalized observable; the audit must fail.

SCL-C03 — Same-ruler comparison and Observer transport

Question. Are all candidates and records compared using the same frozen ruler tuple and the same Observer map?

Freeze \[ \mathfrak R=(D{\rm parent},D{\rm obs},F,\mu,{\cal S},N{\rm bundle},N{\rm field},G_{\rm global},\Pi,\Lambda,\Delta,\mathcal T,\mathcal O). \] Comparison is admissible only when the tuples are identical or a complete invertible/controlled transport is supplied.

Required inputs

candidate ruler tuples;
Observer certificate;
scheme/frame transports;
observable definitions;

Execution algorithm

hash each ruler tuple.
align dimensions, frames, scale, scheme and normalizations.
transport covariance and truncation errors.
run wrong-ruler negative control.

Required outputs

samerulerpacket;
uncertaintycovariancepacket;

Minimal discharge. Shared ruler hash or explicit transport chain with uncertainty propagation and inverse/consistency check.

Fail trigger. Raw parent quantities, different chambers, different schemes, or different observable definitions are compared directly.

Destructive control. Use a one-chamber 4D running mass against an unprojected higher-dimensional norm; the audit must fail.

SCL-C04 — Structural information versus absolute scale and anchor identifiability

Question. Does the derivation distinguish dimensionless structural relations from the independent anchors required to assign absolute magnitudes?

If Shape fixes a relation $f(x1,\ldots,xn)=0$, Scale must compute the rank of the scale-identification map. Absolute prediction requires the number of independent anchors to equal the unresolved dimensional rank and the inverse map to be identifiable.

Required inputs

structural relations;
dimension matrix;
anchor list;
Jacobian of observable map;

Execution algorithm

separate dimensionless and dimensionful relations.
compute rank/nullity of the dimension matrix.
identify the minimal anchor set.
test local/global identifiability and degeneracy.

Required outputs

anchoridentifiabilitypacket;
provenance_ledger;

Minimal discharge. Rank calculation showing exactly which absolute magnitudes are derived and which remain measured/calibrated/global inputs.

Fail trigger. A topology, ratio, or normalization convention is presented as creating an absolute physical unit.

Destructive control. Give all dimensionless ratios but no independent mass/length anchor; absolute masses must remain OPEN.

SCL-C05 — Background scale versus physical fluctuation

Question. For every geometric or environmental scale, is the background value separated from its physical fluctuation, kinetic normalization, potential, mass, mixing, and Observer coupling?

For each scale $Ra$, publish \[ Ra=Ra^{(0)}+Za^{-1/2}\,\delta Ra \] and classify $\delta Ra$ as gauge, constrained, external, massive, massless, tachyonic, or absent by a type theorem.

Required inputs

Shape deformation basis;
Dynamics Hessian;
Rigidity certificate;
Observer coupling map;

Execution algorithm

enumerate all scale-bearing backgrounds.
construct fluctuation variables and kinetic form.
apply constraints/gauge quotient.
compute mass/mixing and response.
require type proof for absence.

Required outputs

radiusradionledger;
gapdecouplingpacket;

Minimal discharge. Complete background/fluctuation ledger with operator, domain, mass/gap, mixing, and response evidence.

Fail trigger. A measured/fixed radius, interval length, boundary position, temperature, or flux is used to assert that its fluctuation is absent or stabilized.

Destructive control. Fix a radius numerically while retaining a flat radion potential; stability must fail.

SCL-C06 — Quantitative gaps, decoupling, and observation windows

Question. Is every omitted physical mode quantitatively separated from the claimed observation window after normalization, mixing, uncertainty, and boundary effects?

For every omitted sector $n$ require \[ m{n,\rm phys}^2-E{\rm max}^2 \ge M_{\rm margin}^2>0 \] with covariance, mixing, loop/matching order, domain, and tail scope included.

Required inputs

physical spectrum;
boundary domains;
mixing matrices;
observation window;
uncertainty covariance;

Execution algorithm

identify the lightest omitted physical eigenvalue per sector.
canonically normalize and diagonalize.
propagate covariance and truncation error.
compare worst-case lower bound to the observation window.
certify tail or limit scope.

Required outputs

gapdecouplingpacket;
towermatchingtail_packet;

Minimal discharge. Sector-by-sector lowest-mode table and robust uncertainty-margin calculation.

Fail trigger. “Compact,” “heavy,” “Planck suppressed,” or central-value separation is used without a quantitative physical gap.

Destructive control. Choose a central gap above the cutoff whose lower confidence bound enters the window; closure must fail.

SCL-C07 — Constraint multiplier versus physical stiffness

Question. Are exact multipliers, constitutive restrictions, penalties, and physical stabilizing couplings kept distinct?

A multiplier term $\lambda\Phi$ and a stiffness term $\kappa\Phi^2/2$ belong to different measure and response classes. A limiting claim $\kappa\to\infty$ requires convergence of the measure, stress, determinants, spectrum, and low-energy observables.

Required inputs

parent action;
constraint classification;
measure/determinant packet;
response functions;

Execution algorithm

classify each enforcing term.
compute whether its coefficient fluctuates or runs.
compare finite-stiffness and exact-constraint measures.
test limiting convergence and residual stress.

Required outputs

multiplierstiffnesspacket;
parameteraccountingpacket;

Minimal discharge. Term-by-term classification with dimensionality, physical status, measure contribution, and limiting proof where invoked.

Fail trigger. A physical stiffness is hidden as a constraint, or an exact multiplier is counted as a tunable physical parameter without justification.

Destructive control. Stabilize a mode with $\kappa\Phi^2/2$ but label $\kappa$ a multiplier; the audit must fail.

SCL-C08 — Equal parameter, discrete-choice, boundary, and global accounting

Question. Are all candidates charged with the same categories of measured, calibrated, physical, structural, global, boundary, matching, constraint, and discrete inputs?

Publish for candidate $i$ \[ \mathcal Pi=(Nm,Nc,Np,Ns,Ng,Nb,N{\rm match},N{\rm con},Nd) \] plus the full object list. No category may be omitted because its values are discrete, topological, global, boundary-localized, or hidden in a definition.

Required inputs

candidate manifests;
provenance ledger;
boundary/global data;
matching packets;

Execution algorithm

enumerate all independent choices.
classify each choice identically across candidates.
detect aliases and hidden inputs.
compare vectors without an undeclared scalar exchange rate.

Required outputs

parameteraccountingpacket;
economyvectorpacket;

Minimal discharge. Equal-category parameter tables and machine check reporting no omitted or differently classified candidate input.

Fail trigger. One candidate is called parameter-free by hiding discrete, global, boundary, normalization, or stiffness choices.

Destructive control. Move a fitted real parameter into a boundary datum and claim improved economy; the comparison must reject it.

SCL-C09 — Complete vacuum and cosmological-term ledger

Question. Are all contributions to the renormalized constant term represented on one scale, frame, scheme, and support ledger?

Require \[ \Lambda{4,\rm ren}=\Lambda{\rm parent}+\Lambda{\rm curv}+\Lambda{\rm flux}+\Lambda{\rm bnd}+\Lambda{\rm matter}+\Lambda{\rm con}+\Lambda{\det}+\Lambda{\rm match}+\Lambda{\rm grav}+\Lambda_{\rm residual}, \] with every term typed, varied where appropriate, and transported consistently.

Required inputs

parent/effective actions;
determinants;
boundary terms;
thresholds;
Vacuum certificate;

Execution algorithm

enumerate all constant terms by support and owner.
transport to one frame/scheme/scale.
record metric dependence and variation status.
include threshold, determinant, graviton and matching terms.
test protected versus accidental cancellations.

Required outputs

vacuumtermledger;
schemergmatching_packet;

Minimal discharge. Complete signed ledger with units, frame, scale, scheme, support, owner, threshold dependence, uncertainty, and protection status.

Fail trigger. Any constant contribution is omitted, double-counted, or cancelled across mismatched schemes without a protecting equation.

Destructive control. Omit the constraint determinant contribution while claiming a complete vacuum cancellation; the audit must fail.

SCL-C10 — Vacuum stability versus residual-value ownership

Question. Are invariance under constant matter shifts and the numerical ownership of the observed residual treated as separate claims?

The stability test is \[ \mathcal Lm\mapsto\mathcal Lm-c\quad\Rightarrow\quad \delta \mathcal O_{\rm local}=0, \] while value ownership requires exactly one of theorem-derived, independently boundary/global fixed, calibrated input, measured residual, or OPEN.

Required inputs

Vacuum response law;
residual value source;
boundary/global equations;
measurement ledger;

Execution algorithm

execute constant-shift response test.
trace residual value provenance independently.
reject double ownership.
state separate terminals for stability and value.

Required outputs

vacuumstabilityvalue_packet;
measuredanchorfirewall_packet;

Minimal discharge. Two independent certificates: constant-shift response and single-owner residual-value classification.

Fail trigger. A measured residual is called predicted, or a stability theorem is claimed to determine its observed magnitude.

Destructive control. Use exact shift protection but insert the residual from observation; stability may pass while prediction must not.

SCL-C11 — Threshold, phase-transition, and history scale ledger

Question. Are heavy thresholds and finite transitions tracked through both static matching and time-dependent history?

For each transition $\alpha$ publish before/after effective actions, matching map, additive shift, latent heat, nonconstant stress, transition duration, temperature/time scale, and residual history effect.

Required inputs

Dynamics history packet;
Vacuum history packet;
threshold spectra;
thermal/phase data;

Execution algorithm

enumerate every threshold and condensate transition.
derive before/after actions.
compute matching and additive shifts.
track finite-time stress and global/boundary response.
propagate to later observables.

Required outputs

thresholdphasehistory_packet;
statedependentscale_packet;

Minimal discharge. Complete chronological threshold/phase ledger with static and dynamical effects separately evaluated.

Fail trigger. A static constant-term cancellation is promoted to compatibility with a finite phase transition or cosmological history.

Destructive control. Cancel constants before and after a transition but retain nonzero latent heat; history must remain nontrivial.

SCL-C12 — Renormalization, scheme, RG, and matching transport

Question. Are scheme-dependent coefficients transported only as part of a complete coupled observable packet?

Under $(\mathbf c,\mu,{\cal S})\mapsto(\mathbf c',\mu',{\cal S}')$, require a transport map for the full effective action/observable vector and covariance, with matching-order and threshold conventions frozen.

Required inputs

beta functions;
matching maps;
scheme transformations;
observable vector;
covariance;

Execution algorithm

freeze loop and truncation order.
transport the coupled coefficient vector.
include operator mixing and thresholds.
propagate covariance and truncation error.
check physical observable invariance within declared scope.

Required outputs

schemergmatching_packet;
uncertaintycovariancepacket;

Minimal discharge. Coupled transport calculation showing scheme/frame dependence cancels or is explicitly retained in the physical prediction.

Fail trigger. An isolated running coefficient, one-scale cancellation, or unmatched loop order is compared as a physical invariant.

Destructive control. Tune two terms to cancel at one renormalization scale with no protecting equation; no stability credit is allowed.

SCL-C13 — Measured-anchor, calibration, prediction, and residual firewall

Question. Is every datum assigned exactly one inferential role, with no training-on-the-test or double counting?

Each observable receives one role in \[ \{\text{measured anchor},\text{calibration input},\text{derived output},\text{blind prediction},\text{measured residual}\}. \] A datum may change role only under a new predeclared experiment and freeze.

Required inputs

observable manifest;
fit/calibration history;
candidate dependence;
uncertainty;

Execution algorithm

assign one role per observable.
record the stage at which it enters.
trace candidate dependence.
exclude calibrated observables from independent prediction counts.
run role-duplication test.

Required outputs

measuredanchorfirewall_packet;
provenance_ledger;

Minimal discharge. Role ledger with zero duplicates and an independent prediction set disjoint from calibration inputs.

Fail trigger. A quantity used to choose/fix the candidate is counted again as a successful prediction.

Destructive control. Fit a mass and then count the same mass as a blind prediction; the audit must fail.

SCL-C14 — Topological and inflow coefficient normalization and quantization

Question. Are dimensionless topological coefficients globally normalized, quantized, and pre-owned rather than tuned?

For coefficient $k$, require $k\in\Lambda_{\rm quant}$ under the declared differential-form, trace, charge-lattice, global-group, quotient, and orientation conventions, and pass all large-gauge tests.

Required inputs

Boundary anomaly/inflow packet;
global gauge group;
charge lattice;
trace/form conventions;

Execution algorithm

construct the quantization lattice.
transport cover/quotient and orientation factors.
test large transformations.
classify counterterm ambiguity.
verify parent provenance before residual inspection.

Required outputs

topologicalcoefficientpacket;
samerulerpacket;

Minimal discharge. Exact coefficient-lattice and large-gauge certificate sharing normalization hashes with Boundary.

Fail trigger. A real coefficient is chosen after the anomaly is computed, or a factor-of-two/sign/quotient mismatch remains.

Destructive control. Choose an unquantized Chern–Simons coefficient that cancels the local residual; global closure must fail.

SCL-C15 — Uncertainty covariance, sensitivity, and identifiability

Question. Are uncertainties, correlations, parameter sensitivities, degeneracies, and truncation errors propagated through the full map?

For output $y=f(x)$ require \[ \Sigmay=Jf\SigmaxJf^T+\Sigma{\rm trunc}+\Sigma{\rm scheme}+\Sigma_{\rm model}, \] and publish rank/condition diagnostics for the inverse or identification map.

Required inputs

input covariance;
Jacobian/sensitivity map;
truncation and scheme errors;
measurement model;

Execution algorithm

assemble full covariance including correlations.
differentiate/linearize or sample the map.
propagate model and truncation uncertainty.
compute rank, condition number, and degeneracy directions.
perform robustness/worst-case test.

Required outputs

uncertaintycovariancepacket;
anchoridentifiabilitypacket;

Minimal discharge. Full covariance and sensitivity packet with degeneracies and confidence margins explicit.

Fail trigger. Only central values or independent errors are compared, or a poorly identifiable output is declared uniquely derived.

Destructive control. Use anticorrelated inputs but propagate them as independent; the audit must detect the wrong uncertainty.

SCL-C16 — Hierarchy, naturalness, and radiative-sensitivity diagnosis

Question. Are large scale separations classified by actual protection, sensitivity, and matching structure rather than aesthetic labels?

For low scale $mL$ and high scales/parameters $xa$, publish \[ \Deltaa=\left|\frac{\partial\ln mL^2}{\partial\ln x_a}\right| \] or a more appropriate invariant sensitivity, together with symmetry, topology, sequestering, fixed-point, or dynamical protection claims.

Required inputs

matching relations;
loop corrections;
symmetry/protection certificates;
parameter covariance;

Execution algorithm

identify all high-scale contributions to low-scale quantities.
compute regulator/scheme-aware sensitivities.
separate coordinate reparameterization from physical tuning.
test proposed protection under thresholds and loops.
classify diagnosis without using economy as a hard gate.

Required outputs

hierarchysensitivitypacket;
schemergmatching_packet;

Minimal discharge. Sensitivity and protection ledger with radiative/threshold robustness and declared claim ceiling.

Fail trigger. A small low-energy scale is called derived or natural solely because a parameter was chosen small or a cancellation occurs at one order.

Destructive control. Tune two high-scale terms to produce a small Higgs mass without protection; the hierarchy remains input-sensitive.

SCL-C17 — Multi-scale EFT, tower matching, truncation, and tail control

Question. Does every finite-mode or finite-operator calculation state its scale interval and control omitted towers/tails?

For nested effective descriptions $\mathcal E0\subset\cdots\subset\mathcal EN$, require matching maps, overlap checks, and a tail certificate $\|RN\|\le\epsilonN$ or an explicit finite-scope ceiling.

Required inputs

tower spectrum;
operator basis;
matching scales;
RG data;
Granularity refinement lattice;

Execution algorithm

partition scale intervals.
match adjacent EFTs.
test overlap and decoupling.
compute omitted-mode/operator tail or bound.
vary truncation/refinement and record convergence.
forbid global promotion without a theorem.

Required outputs

towermatchingtail_packet;
resolutionrefinementpacket;

Minimal discharge. Nested matching ledger and convergence/tail certificate with explicit validity interval.

Fail trigger. A zero-mode, finite tower, or finite heat-kernel prefix is promoted to an all-scale claim.

Destructive control. Construct two identical finite prefixes with convergent and divergent tails; global inference must remain OPEN.

SCL-C18 — Time, temperature, horizon, correlation, and state-dependent scales

Question. Are scales that depend on state, history, region, horizon, temperature, or synchronization treated as derived fields/records rather than fixed universal constants?

For derived scale $s[\Psi,g,\rho,t,U]$, publish its defining functional, covariance, support, synchronization convention, variation, and domain of validity.

Required inputs

Dynamics histories;
Boundary derived supports;
Time Synchronization packet;
Observer regional records;

Execution algorithm

enumerate state-/region-dependent scale definitions.
derive them from frozen states and supports.
transport clocks/temperatures/redshifts consistently.
compute variation and uncertainty.
test across transitions and horizon/interface changes.

Required outputs

statedependentscale_packet;
samerulerpacket;

Minimal discharge. Definition and transport packet for every nonconstant scale, including support, time standard, and uncertainty.

Fail trigger. A local temperature, horizon radius, correlation length, clock rate, or transition scale is treated as one global fixed ruler.

Destructive control. Use a single coordinate time or temperature across redshifted regions; the same-ruler test must fail.

SCL-C19 — Composite, emergent, and effective scale provenance

Question. Are bound-state masses, condensate scales, correlation lengths, soliton sizes, and emergent effective cutoffs derived from constituent dynamics rather than silently promoted to primitive inputs?

For emergent scale $ME$, require a derivation/definition map \[ ME=F(\text{Actors},\text{interactions},\text{state},\mu,\text{scheme}) \] with double-counting and matching checks when an effective Actor is promoted.

Required inputs

Actor promotion packet;
interaction hypergraph;
state/condensate data;
matching scheme;

Execution algorithm

enumerate effective/composite scales.
identify constituent and interaction ownership.
derive or calibrate the scale explicitly.
check matching and double counting.
state the EFT validity interval.

Required outputs

emergentscalepacket;
parameteraccountingpacket;

Minimal discharge. Constituent-to-effective scale derivation and no-double-counting certificate.

Fail trigger. A composite/effective mass or cutoff is treated as a new primitive anchor without provenance or while its constituents remain independently counted.

Destructive control. Introduce a bound-state mass as an independent parameter after deriving it from constituents; the ledger must flag double ownership.

Question. Do scale cutoffs, observational resolution, discretization, and Granularity classes form a monotone refinement system?

For refinement order $r1\preceq r2$, require compatible maps \[ \mathcal Q{r2}\to\mathcal Q{r1} \] and monotone/controlled behavior of records, equivalence classes, spectra, and uncertainties.

Required inputs

Granularity cell signatures;
cutoff/refinement ladder;
Observer resolutions;
Dynamics truncations;

Execution algorithm

freeze the refinement poset.
compute coarse-graining/projection maps.
test class consistency and noncommuting limits.
track discretization and cutoff errors.
require convergence or scope ceiling.

Required outputs

resolutionrefinementpacket;
towermatchingtail_packet;

Minimal discharge. Commuting refinement diagram and error/convergence ledger shared with Granularity and Dynamics.

Fail trigger. Changing cutoff/resolution changes the claimed physical class without being detected, or noncommuting limits are silently exchanged.

Destructive control. Take continuum and infinite-volume limits in opposite orders when they disagree; global closure must fail.

SCL-C21 — Candidate-neutral scale grammar, saturation, and exhaustion

Question. Has every scale-bearing object, anchor choice, matching scale, cutoff, threshold, normalization, and admissible scale route been generated and given a disposition?

Define a frozen grammar $\mathcal G{\rm scl}$ and require \[ N{\rm ungenerated}=N{\rm unclassified}=N{\rm unresolved\ aliases}=N_{\rm omitted\ scale\ routes}=0 \] within the declared scope.

Required inputs

Shape/Actor grammar;
Dynamics operators and histories;
Boundary supports;
Observer/Granularity test families;

Execution algorithm

generate all scale objects by typed grammar.
canonicalize aliases and convention duplicates.
assign provenance and owner.
test omitted anchors, thresholds, cutoffs, schemes and scale routes.
publish saturation residual.

Required outputs

scalegrammarexhaustion_packet;
residualvectorpacket;

Minimal discharge. Machine-generated complete scale roster with zero unclassified rows and omitted-route controls.

Fail trigger. One convenient scale assignment or one successful matching route is treated as exhaustive without grammar or theorem.

Destructive control. Add an admissible boundary scale or matching route omitted from the roster; the exhaustion residual must become nonzero.

SCL-C22 — Economy and representative-selection firewall

Question. Is economy used only after physical equivalence and without an undeclared exchange rate among dimensions, parameters, computations, and assumptions?

For physically equivalent candidates publish a vector \[ \mathbf w=(D,Nm,Nc,Np,Nd,Nb,L{\rm desc},C_{\rm comp}) \] and use a scalar order only if frozen independently of outcomes.

Required inputs

physical equivalence certificate;
parameter ledgers;
description/computation metrics;
ordering rule;

Execution algorithm

require hard-physics pass first.
publish economy vector.
freeze any lexicographic/partial order.
test invariance under representation changes.
forbid economy from rescuing a failed constraint.

Required outputs

economyvectorpacket;
gatescalesummary;

Minimal discharge. Economy vector and predeclared ordering applied only among one physical equivalence class.

Fail trigger. Simplicity, fewer dimensions, or cheaper computation is used to select a physically failing or distinguishable candidate.

Destructive control. Give the physically wrong candidate a shorter description; it must still lose.

SCL-C23 — Scale-transformation covariance, homogeneity, and anomalous dimensions

Question. Does every scale-bearing field, operator, observable, spectrum, and response come with its transformation law under a change of physical scale, rather than only a value at one reference point?

Formal requirement.

For each typed object $Oi$ and admissible scale transport $s\mapsto \lambda s$ or $\mu\mapsto e^t\mu$, require a controlled representation \[ Oi(\lambda s)=\lambda^{\Deltai^{\rm can}}\sumj U{ij}(\lambda)Oj(s), \qquad \gamma{ij}=\frac{d}{d\ln\lambda}U{ij}\bigg|_{\lambda=1}, \] with canonical dimensions, anomalous-dimension/mixing data, normalization transport, reference/pivot scale, validity interval, and residuals explicit.

Required inputs.

typed operator/observable roster;
canonical dimensions;
RG or physical scaling map;
normalization and mixing matrices;
reference/pivot scales;

Execution algorithm.

generate every admissible physical scale transformation.
derive canonical homogeneity degrees.
compute or import anomalous dimensions and operator mixing.
transport normalizations and covariance.
test slopes/exponents over the claimed interval rather than one calibration point.
publish residuals and scope ceiling.

Required outputs. scaletransformationpacket.

Minimal witness. A complete transformation-law ledger with canonical/anomalous dimensions, mixing, pivot/reference scales, interval tests, and zero unclassified scale responses.

Fail trigger. Two candidates agree at one scale but differ in scaling law, anomalous dimension, or homogeneity and are nevertheless treated as physically equivalent.

Destructive control. Construct two models with the same observable at one pivot scale but different anomalous dimensions; the audit must distinguish them.

SCL-C24 — Scale-symmetry breaking, trace/Weyl anomaly, and dimensional transmutation

Question. Are explicit, spontaneous, and anomalous breaking of scale symmetry separated, and are dynamically generated invariant scales derived rather than silently inserted as primitive anchors?

Formal requirement.

Require a scale Ward identity of the form \[ \left(\mu\partial\mu+\beta^a\partial{g^a}-\gammai\mathcal Ni\right)\Gamma =\mathcal A{\rm scale}+\mathcal B{\rm explicit}, \] and, when dimensional transmutation is claimed, an RG-invariant generated scale such as \[ \Lambda=\mu\exp\!\left[-\int^{g(\mu)}\frac{dg}{\beta(g)}\right] \] with scheme, threshold, measure/Jacobian, boundary, and vacuum provenance controlled.

Required inputs.

effective action and measure;
beta and anomalous-dimension data;
explicit breaking terms;
Boundary/Vacuum anomaly ledgers;
candidate generated scales;

Execution algorithm.

derive the scale/dilatation Ward identity.
separate explicit, spontaneous, and anomalous breaking.
compute trace/Weyl anomaly and measure contributions.
derive every RG-invariant generated scale.
test scheme/path/threshold invariance within scope.
route vacuum and boundary contributions to their owners.

Required outputs. scaleanomalytransmutationpacket, emergentscalepacket, schemergmatchingpacket.

Minimal witness. A Ward-identity and generated-scale certificate proving the provenance and scoped invariance of every transmuted scale and every trace/Weyl anomaly term.

Fail trigger. A confinement, Planck, vacuum, or other generated scale is called derived without a scale Ward identity/transmutation map, or a trace anomaly is omitted from the scale ledger.

Destructive control. Give two theories the same coupling at one renormalization scale but different beta functions; their generated invariant scales must not be identified.

SCL-C25 — Criticality, universality, finite-size scaling, and crossover

Question. Are claims near fixed points, phase transitions, continuum limits, or thermodynamic limits supported by critical exponents, universality data, finite-size scaling, and crossover control?

Formal requirement.

For control parameter $t$, size $L$, and correlation length $\xi$, require the applicable scaling form, for example \[ \xi\sim |t|^{-\nu},\qquad \Delta(L,t)=L^{-z}F\!\left(L^{1/\nu}t,\{uiL^{-\omegai}\}\right), \] with the fixed point, relevant/irrelevant directions, critical and dynamical exponents, boundary conditions, regulator family, and crossover domain specified.

Required inputs.

RG fixed-point/flow data;
order/control parameters;
finite-volume and boundary spectra;
thermal/history data;
Granularity refinement lattice;

Execution algorithm.

identify candidate fixed points and universality classes.
linearize the flow and compute relevant/irrelevant directions.
derive critical and dynamical exponents.
perform finite-size/refinement scaling tests.
compute crossover functions and validity regions.
test regulator, boundary, and microscopic-detail independence.

Required outputs. criticalscalinguniversalitypacket, resolutionrefinementpacket, statedependentscalepacket.

Minimal witness. A universality certificate with fixed point, exponents, finite-size scaling, crossover, regulator/boundary tests, and explicit unresolved directions.

Fail trigger. A finite-volume gap, one correlation length, one truncation fixed point, or one phase-transition point is promoted to a continuum universality claim.

Destructive control. Construct two models with the same correlation length at one point but different $ u$ or $z$; the audit must keep them distinct.

SCL-C26 — Extensive, intensive, area/volume/fractal scaling, and regional composition

Question. Do regional, thermodynamic, entropic, geometric, and information quantities obey the correct scaling and composition law across changes of region size and shape?

Formal requirement.

For a scaled region $\lambda U$, require a typed decomposition such as \[ Q(\lambda U)=\lambda^{d{\rm bulk}}Q{\rm bulk}(U)+\lambda^{d{\partial}}Q{\partial}(\partial U)+Q{\rm corner}+Q{\rm top}+Q_{\rm nonlocal}, \] with extensive/intensive/subextensive class, area/volume/fractal or spectral exponent, finite-size corrections, and disjoint-region composition/mutual terms explicit.

Required inputs.

regional supports and incidence data;
Boundary edge/corner packets;
Observer regional records;
entropy/information/thermodynamic quantities;
state-dependent scales;

Execution algorithm.

classify each quantity as extensive, intensive, subextensive, topological, or nonlocal.
separate bulk, boundary, corner, defect, and mutual contributions.
derive area/volume/fractal/spectral exponents.
test disjoint-region composition and finite-size corrections.
transport uncertainty and state dependence.
state the scaling domain and residuals.

Required outputs. compositionscalingpacket, statedependentscalepacket, resolutionrefinement_packet.

Minimal witness. A regional composition certificate showing the correct scaling exponent and decomposition over multiple region sizes/shapes, with boundary and nonlocal corrections included.

Fail trigger. Two models agree for one region but have different area/volume/extensive scaling and are treated as equivalent, or boundary/mutual terms are hidden in a bulk coefficient.

Destructive control. Match two entropy models at one horizon area, one scaling as area and the other as volume; the audit must reject equivalence.

7. Cross-block compilation pipeline

Scale is executed after candidate generation but before any numerical comparison is credited:

Shape import: supports, Actors, discrete choices, topology, deformation basis, and state-dependent supports.
Dynamics import: physical operators, spectra, masses, interactions, histories, RG data, and regional fluxes.
Boundary import: domains, quotient factors, fixed-set measures, topological/inflow coefficients, horizon/interface supports.
Rigidity import: physical deformation classification and stability eigenvalues.
Vacuum import: background equations, constant-shift response, threshold history, residual ownership candidates.
Observer/TS import: parent-to-record map, measurement resolution, units, clocks, redshifts, and covariance.
Granularity import: equivalence-cell and refinement lattice, candidate/test exhaustion scope.
Scale compile: generate the complete scale grammar, assign provenance, align the ruler, derive scale-transformation laws and anomalies, compute critical/universality and regional-composition data, transport uncertainties, compute gaps and ledgers, run controls, and issue packets.

No downstream block may select a scale, scheme, cutoff, tolerance, or normalization after inspecting the desired residual.

8. Complete execution order

Freeze authorities, gate contract, candidate grammar, ruler tuple, observable roles, and uncertainty policy.
Generate every scale-bearing object from Shape, Dynamics, Boundary, Observer, Vacuum, Rigidity, and TS.
Assign primary provenance and owner; run orphan/duplicate tests.
Run dimensional/frame/normalization closure.
Reconstruct anchors and identifiability rank.
Build scale-versus-field and radius/radion ledger.
Compute physical gaps, observation windows, and tower/tail scope.
Classify multipliers, stiffnesses, parameters, and discrete choices.
Construct complete vacuum and threshold/history ledgers.
Transport all coupled quantities across scheme, RG, frame, and matching maps.
Apply measured-anchor/calibration/prediction firewall.
Quantize topological/inflow coefficients with Boundary.
Propagate covariance, sensitivities, hierarchy diagnostics, and robustness.
Build state-dependent and emergent scale packets.
Check resolution/refinement commutation and noncommuting limits.
Derive scale-transformation laws, canonical/anomalous dimensions, and homogeneity tests.
Derive the scale Ward identity, trace/Weyl anomaly ledger, and every transmuted invariant scale.
Execute critical/universality, finite-size, and crossover tests where applicable.
Execute extensive/intensive and area/volume/fractal regional-composition tests where applicable.
Prove scale-grammar saturation or retain explicit OPEN residuals.
Run all destructive controls.
Issue V3/V4 compatibility certificates, integrated V4.1 certificate, residual vector, claim ceiling, and reopen triggers.

9. Required evidence bundle

Every gate execution must produce all 35 packet types. Nonapplicable packets remain present with status: NOT-APPLICABLE and a type proof.

`scaleauthoritymanifest`

Required fields:

authority_id;
version;
authority_hash;
companion_hashes;
gate_id;
freeze_hash;

`provenance_ledger`

Required fields:

objects;
allowed_classes;
owner_uniqueness;
orphan_count;
mutation_check;

`samerulerpacket`

Required fields:

ruler_tuple;
tuple_hash;
transport_steps;
observer_hash;
consistency_checks;

`dimensionalclosurepacket`

Required fields:

unit_basis;
equations;
dimension_vectors;
frame_maps;
normalization_maps;
residuals;

`anchoridentifiabilitypacket`

Required fields:

structural_relations;
dimension_matrix;
rank;
nullity;
anchors;
jacobian;
degeneracies;

`radiusradionledger`

Required fields:

scale_sectors;
background_values;
fluctuations;
kinetic_forms;
constraints;
masses;
mixings;
observer_couplings;

`gapdecouplingpacket`

Required fields:

observation_window;
sector_gaps;
mixing;
uncertainty_margin;
tail_scope;
verdict;

`multiplierstiffnesspacket`

Required fields:

terms;
classification;
dimensions;
measure_effects;
stress;
limit_tests;

`parameteraccountingpacket`

Required fields:

candidate_vectors;
object_lists;
alias_checks;
equalcategorycheck;

`vacuumtermledger`

Required fields:

terms;
frame;
scale;
scheme;
support;
owners;
metric_dependence;
threshold_dependence;
uncertainty;
protection;

`vacuumstabilityvalue_packet`

Required fields:

constantshifttest;
local_response;
residual_owner;
doubleownercheck;
separate_verdicts;

`thresholdphasehistory_packet`

Required fields:

thresholds;
beforeafteractions;
matching;
constant_shifts;
latent_heat;
time_scales;
history_effects;

`schemergmatching_packet`

Required fields:

coefficient_vector;
beta_functions;
scheme_maps;
matching_maps;
operator_mixing;
thresholds;
observable_invariance;

`measuredanchorfirewall_packet`

Required fields:

observables;
roles;
input_stages;
candidate_dependence;
prediction_set;
duplicaterolecount;

`topologicalcoefficientpacket`

Required fields:

terms;
form_norms;
trace_norms;
global_groups;
charge_lattices;
coefficient_lattices;
largegaugetests;
quotient_factors;
orientations;
parent_provenance;

`uncertaintycovariancepacket`

Required fields:

input_covariance;
jacobian;
truncation_error;
scheme_error;
model_error;
output_covariance;
condition_numbers;
robustness;

`hierarchysensitivitypacket`

Required fields:

low_scales;
high_inputs;
sensitivity_measure;
loop_order;
thresholds;
protection_mechanisms;
scheme_checks;
verdict;

`towermatchingtail_packet`

Required fields:

scale_intervals;
effective_theories;
matching_maps;
overlap_tests;
omitted_tails;
tail_bounds;
scope_ceiling;

`statedependentscale_packet`

Required fields:

scale_definitions;
states;
supports;
time_standards;
temperatureredshiftmaps;
variations;
uncertainty;

`emergentscalepacket`

Required fields:

effective_scales;
constituents;
interactions;
derivations;
calibrations;
doublecountingchecks;
validity_intervals;

`resolutionrefinementpacket`

Required fields:

refinement_poset;
projection_maps;
commutation_tests;
limitordertests;
errors;
convergence;

`scalegrammarexhaustion_packet`

Required fields:

grammar;
generated_roster;
aliases;
dispositions;
omittedroutecontrols;
residual_counts;

`economyvectorpacket`

Required fields:

equivalence_class;
vectors;
ordering_rule;
representation_invariance;
nongatingcheck;

`scalecertificatev3_compatibility`

Required fields:

candidate_id;
samerulertuple;
measured_anchors;
calibration_inputs;
derived_scales;
radiusradionledger;
compactification_gap;
observation_window;
fieldandbundle_normalizations;
renormalization_scale;
schemeandmatching_order;
cutoffandfloor;
constraintmultiplierdimensions;
physicalstiffnessparameters;
determinant_contributions;
cosmologicaltermledger;
thresholdandphasetransitionledger;
residuallambdaowner;
uncertainty_covariance;
parameter_ledger;
evidence_hashes;
verdict;

`integratedscalecertificate_v4`

Required fields:

gate_id;
authority_manifest;
constraintrowstates;
packet_hashes;
residual_vector;
claim_ceiling;
terminal;
reopen_triggers;

`residualvectorpacket`

Required fields:

unowned;
dimension_mismatches;
wrong_rulers;
unidentified_anchors;
unclassified_fluctuations;
unbounded_gaps;
hidden_stiffness;
omitted_parameters;
vacuum_omissions;
double_roles;
unquantized_coefficients;
uncontrolled_uncertainties;
unstable_hierarchies;
unbounded_tails;
statescaleerrors;
emergentdoublecounts;
refinement_failures;
unexhaustedscaleroutes;

`destructivecontrolspacket`

Required fields:

controls;
expected_outcomes;
actual_outcomes;
failures;

`gatescalesummary`

Required fields:

gate_id;
physical_question;
selected_constraints;
inputs;
outputs;
findings;
external_dependencies;
claim_ceiling;
terminal;

`dependency_hashes`

Required fields:

shape;
granularity;
dynamics;
boundary;
observer;
rigidity;
vacuum;
time_synchronization;
gate_contract;

`validator_output`

Required fields:

validator_version;
checks;
errors;
warnings;
status;

`scaletransformationpacket`

Required fields:

objects;
scale_transformations;
canonical_dimensions;
anomalousdimensionmatrix;
operator_mixing;
normalization_transport;
referenceorpivot_scales;
validity_intervals;
homogeneity_tests;
residuals;

`scaleanomalytransmutation_packet`

Required fields:

ward_identity;
explicit_breaking;
spontaneous_breaking;
measure_jacobian;
traceorweyl_anomaly;
beta_functions;
generatedinvariantscales;
schemepathtests;
thresholdandboundary_terms;
vacuum_terms;
residuals;

`criticalscalinguniversality_packet`

Required fields:

control_parameters;
order_parameters;
fixed_points;
linearized_flow;
critical_exponents;
dynamical_exponent;
relevantirrelevantdirections;
finitesizescaling;
crossover_functions;
boundaryregulatortests;
universality_verdict;
residuals;

`compositionscalingpacket`

Required fields:

regions;
scaling_operations;
bulk_terms;
boundary_terms;
cornerdefectterms;
topological_terms;
nonlocalmutualterms;
extensiveintensiveclass;
areavolumefractal_exponents;
composition_tests;
finitesizecorrections;
residuals;

`integratedscalecertificatev41`

Required fields:

gate_id;
authority_manifest;
constraintrowstates;
packet_hashes;
v40compatibility;
sourcetermcoverage;
residual_vector;
claim_ceiling;
terminal;
reopen_triggers;

10. Compatibility certificate

scalecertificatev3compatibility preserves every field of scalecertificatev3. The V4 and V4.1 integrated certificates may add fields but may not omit, weaken, or silently reinterpret a V3 field. integratedscalecertificatev4_1 must also prove compatibility with V4.0 and include source-term coverage for SCL-C23–SCL-C26.

11. Residual and terminal logic

Define \[ \mathcal R{\rm SCL}=(N{\rm unowned},N{\rm dim},N{\rm ruler},N{\rm anchor},N{\rm fluct},N{\rm gap},N{\rm stiffness},N{\rm param},N{\rm vacuum},N{\rm role},N{\rm quant},N{\rm unc},N{\rm hierarchy},N{\rm tail},N{\rm state},N{\rm emergent},N{\rm refine},N{\rm transform},N{\rm anomaly},N{\rm critical},N{\rm composition},N_{\rm exhaust}). \] A full scoped Scale PASS requires every applicable component to vanish and all required companion certificates to be valid.

Allowed row states are PASS, FAIL, OPEN, NOT-EVALUATED, NOT-APPLICABLE, CONSTRUCTION-ANCHOR, CONDITIONAL, and RESTART-REQUIRED. Missing evidence is never inferred as zero.

12. Universal anti-promotion rules

A structural ratio is not an absolute magnitude.
A fixed background value is not an absent or stabilized fluctuation.
A qualitative compactification statement is not a quantitative gap.
A multiplier is not a physical stiffness and a stiffness is not an exact constraint.
A discrete/global/boundary choice is not free merely because it is not continuous.
A one-scale cancellation is not a radiative identity.
Vacuum stability is not residual-value prediction.
Static cancellation is not finite transition-history compatibility.
A scheme-dependent coefficient is not an observable.
A calibrated input is not a blind prediction.
A dimensionless inflow coefficient is not automatically quantized or owned.
Central values are not a covariance-aware comparison.
A small number is not a protected hierarchy.
A finite prefix or tower is not an all-scale theorem.
A local clock, temperature, horizon, or correlation scale is not a universal fixed ruler.
An emergent scale is not a primitive anchor without a promotion certificate.
A resolution-dependent equivalence class is not stable without refinement checks.
One tested scale assignment is not an exhausted grammar.
Agreement at one pivot/reference scale is not agreement of the scaling law.
Canonical dimension is not the full anomalous dimension or operator-mixing law.
A generated scale is not derived without a scale Ward identity and transmutation map.
A finite-volume or one-truncation fixed point is not a universality theorem.
Agreement for one region size is not agreement of area/volume/extensive composition.
Economy cannot rescue a physical failure.

13. All-gate profile rule

The machine-readable controlling map is 02REGISTRIES/SCALEGATECROSSWALKV41.json. Every gate bundle contains all 35 packet types. activepackets must be executed; every inactive packet remains present with NOT-APPLICABLE and a gate-specific type proof. Implied Scale relevance is insufficient.

Black-hole-singularity

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C06, SCL-C09, SCL-C10, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C26
Active packets: anchoridentifiabilitypacket, compositionscalingpacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, vacuumstabilityvaluepacket, vacuumtermledger, validator_output
Discipline: Horizon, curvature, clock, regional, cutoff, and information scales are derived and state-dependent; continuum dissolution cannot erase finite regional scale obligations.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Born-rule

Role: CONDITIONAL/SCOPED
Rows: SCL-C03, SCL-C13, SCL-C15, SCL-C18, SCL-C20, SCL-C21, SCL-C22
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, economyvectorpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Measurement resolution, calibration roles, subsystem scales, and probability-record normalizations must be frozen without circular use of observed frequencies.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Gap-01

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C24
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, topologicalcoefficientpacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Heat-kernel coefficients, cutoffs, dimensions, boundary normalizations, schemes, and finite-prefix scope require one ruler and explicit tail control.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Gap-02

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C17, SCL-C20, SCL-C21, SCL-C24, SCL-C25
Active packets: anchoridentifiabilitypacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, schemergmatchingpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: A mass-gap claim requires a physical normalized gap, infinite-volume/continuum order control, refinement stability, and an honest external-wall ceiling.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Gap-05-stability

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C09, SCL-C10, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C24
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, vacuumstabilityvaluepacket, vacuumtermledger, validator_output
Discipline: Static vacuum-offset protection, radiative/threshold robustness, phase history, and residual ownership must remain separate.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Gap-05-value

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C09, SCL-C10, SCL-C13, SCL-C15, SCL-C21, SCL-C24
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, schemergmatchingpacket, uncertaintycovariancepacket, vacuumstabilityvaluepacket, vacuumtermledger, validatoroutput
Discipline: The measured residual requires exactly one owner and may not be counted as a prediction or as evidence of stability.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Gap-08

Role: SCOPED
Rows: SCL-C03, SCL-C04, SCL-C13, SCL-C15, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C25
Active packets: anchoridentifiabilitypacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Any dissolution of an assumed early scale must retain explicit clock, temperature, horizon, observation, and anchor roles.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Gap-10/BG-10

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C25
Active packets: anchoridentifiabilitypacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Baryogenesis needs thermal, reaction-rate, Hubble, washout, transition, and observational scales on one chronological ruler.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Gap-11

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C19, SCL-C20, SCL-C21, SCL-C23
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, parameteraccountingpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Production, freeze-out, abundance, composite-state, and detector scales require full thermal history and matching.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Gap-13

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C19, SCL-C20, SCL-C21, SCL-C23, SCL-C26
Active packets: anchoridentifiabilitypacket, compositionscalingpacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, parameteraccountingpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Entropy, Page time, horizon area, UV cutoff, microstate, and evaporation scales must be consistently derived and regionally transported.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

Lambda-catastrophe

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C09, SCL-C10, SCL-C11, SCL-C12, SCL-C13, SCL-C15, SCL-C16, SCL-C20, SCL-C21, SCL-C23, SCL-C24, SCL-C26
Active packets: anchoridentifiabilitypacket, compositionscalingpacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, vacuumstabilityvaluepacket, vacuumtermledger, validator_output
Discipline: The complete constant-term ledger, shift stability, threshold history, scheme transport, and residual ownership are indispensable.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-1

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C04, SCL-C05, SCL-C08, SCL-C15, SCL-C20, SCL-C21, SCL-C22, SCL-C23
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, economyvectorpacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, parameteraccountingpacket, provenanceledger, radiusradionledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Geometry selection requires honest anchor counts, radii/fluctuation separation, candidate-neutral scale grammar, and non-gating economy.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-10

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Precision and threshold claims require tower matching, loop/scheme consistency, sensitivity, and omitted-tail control.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-2

Role: SUPPORTING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C04, SCL-C06, SCL-C13, SCL-C15, SCL-C21
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Gauge-algebra counting is mainly exact, but normalization, cutoff scope, and measured-anchor firewalls remain required for physical interpretation.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-3

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C04, SCL-C06, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, topologicalcoefficientpacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Family multiplicity and mirror exclusion require normalized index conventions, cutoff/tower scope, and quantified first mirror-capable excitation.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-4

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C12, SCL-C14, SCL-C15, SCL-C21
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, schemergmatchingpacket, topologicalcoefficientpacket, uncertaintycovariancepacket, validator_output
Discipline: Charge and anomaly ledgers require common hypercharge/trace/global-quotient normalization and quantized coefficient provenance.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-5

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C05, SCL-C06, SCL-C07, SCL-C08, SCL-C11, SCL-C12, SCL-C13, SCL-C15, SCL-C16, SCL-C17, SCL-C21, SCL-C23, SCL-C24
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, economyvectorpacket, emergentscalepacket, gapdecouplingpacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, multiplierstiffnesspacket, parameteraccountingpacket, provenanceledger, radiusradionledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: EWSB and hierarchy require complete mass/mixing normalization, physical stiffness ownership, threshold history, sensitivity, and tower matching.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-6

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C05, SCL-C06, SCL-C07, SCL-C08, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C25
Active packets: anchoridentifiabilitypacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, economyvectorpacket, gapdecouplingpacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, multiplierstiffnesspacket, parameteraccountingpacket, provenanceledger, radiusradionledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Moduli claims require every geometric scale fluctuation, kinetic term, potential, mass, mixing, threshold and refinement route.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-7

Role: LOAD-BEARING
Rows: SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C13, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, gapdecouplingpacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Threshold diagnostics must distinguish a wrong-ruler or scope issue from a genuine physical mismatch and cannot use fitted inputs twice.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-8

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C08, SCL-C11, SCL-C12, SCL-C13, SCL-C15, SCL-C16, SCL-C17, SCL-C19, SCL-C20, SCL-C21, SCL-C23
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, economyvectorpacket, emergentscalepacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, parameteraccountingpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Flavor transport is a flagship same-ruler problem: 13D-to-4D projection, running masses, chamber factors, calibration roles, and uncertainties must be explicit.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SG-9

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C24
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gapdecouplingpacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, thresholdphasehistorypacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Proton safety requires operator-suppression scales, thresholds, running, tower effects, matrix-element normalization, and uncertainty margins.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

UQF-10

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C05, SCL-C06, SCL-C07, SCL-C08, SCL-C12, SCL-C15, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C25
Active packets: anchoridentifiabilitypacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, economyvectorpacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, multiplierstiffnesspacket, parameteraccountingpacket, provenanceledger, radiusradionledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Compactification consistency requires full radius/radion, gap, multiplier/stiffness, tower, and refinement ledgers.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

UQF-14

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C25, SCL-C26
Active packets: anchoridentifiabilitypacket, compositionscalingpacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Unitarity claims are scale- and continuation-dependent and require physical energy windows, regulator/refinement stability, and causal clock conventions.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

UQF-3

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C20, SCL-C21, SCL-C25, SCL-C26
Active packets: anchoridentifiabilitypacket, compositionscalingpacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, schemergmatchingpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Reflection positivity requires Euclidean/physical normalization, regulator and continuum-limit ordering, and state/temperature scale control.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

UQF-4

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C12, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, schemergmatchingpacket, topologicalcoefficientpacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Relative/global anomaly and inflow claims require globally quantized coefficients, quotient factors, determinant scales, and regulator/tower scope.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

UQF-5A/5B

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C24
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gapdecouplingpacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Graviton pole/residue and infrared claims require normalized energy windows, analytic-continuation conventions, higher-mode gaps, and truncation stability.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

UQF-5C

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C25
Active packets: anchoridentifiabilitypacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: A UV-completion claim cannot be inferred from a finite coefficient or truncation; nested-scale convergence and regulator independence are mandatory.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

UQF-7

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C04, SCL-C06, SCL-C12, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21
Active packets: anchoridentifiabilitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, schemergmatchingpacket, topologicalcoefficientpacket, towermatchingtailpacket, uncertaintycovariancepacket, validatoroutput
Discipline: Chiral projection requires common index/charge normalization, mirror gap and tower scope, and boundary/global coefficient consistency.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

UQF-9

Role: LOAD-BEARING
Rows: SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C24, SCL-C25
Active packets: anchoridentifiabilitypacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gapdecouplingpacket, gatescalesummary, integratedscalecertificatev4, integratedscalecertificatev41, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, topologicalcoefficientpacket, towermatchingtailpacket, uncertaintycovariancepacket, validator_output
Discipline: Heat-kernel/UV data require dimension, boundary, normalization, matching, finite-prefix and tail discipline.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

theta-bar-QCD

Role: LOAD-BEARING
Rows: SCL-C01, SCL-C02, SCL-C03, SCL-C09, SCL-C10, SCL-C12, SCL-C14, SCL-C15, SCL-C16, SCL-C20, SCL-C21, SCL-C23, SCL-C24, SCL-C25
Active packets: anchoridentifiabilitypacket, criticalscalinguniversalitypacket, dependencyhashes, destructivecontrolspacket, dimensionalclosurepacket, emergentscalepacket, gatescalesummary, hierarchysensitivitypacket, integratedscalecertificatev4, integratedscalecertificatev41, measuredanchorfirewallpacket, provenanceledger, residualvectorpacket, resolutionrefinementpacket, samerulerpacket, scaleanomalytransmutationpacket, scaleauthoritymanifest, scalecertificatev3compatibility, scalegrammarexhaustionpacket, scaletransformationpacket, schemergmatchingpacket, statedependentscalepacket, topologicalcoefficientpacket, towermatchingtailpacket, uncertaintycovariancepacket, vacuumstabilityvaluepacket, vacuumtermledger, validator_output
Discipline: Topological angle, determinant phase, anomaly normalization, radiative stability, and measured residual roles require one global scale/provenance ledger.
Claim ceiling: No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

14. Legacy BB-SCL-4.0 and BB-SCL-3.3 preservation theorem

BB-SCL-4.0 is preservation-complete relative to BB-SCL-3.3 only when:

the exact archival source hash matches the recorded hash;
every legacy section maps to a normative V4 section or compatibility packet;
every old negative control and falsifier remains executable;
every scalecertificatev3 field is present;
the boundary/orbifold coefficient authority and Observer ruler ownership remain binding;
the shared status grammar and anti-promotion rules remain available;
the preservation residual is zero;

The preservation matrix and validator provide the machine check.

15. Reopen triggers

SCL-C01: Any load-bearing quantity is unowned, multiply primary-owned, retrospectively reclassified, or supplied only by the desired gate result.
SCL-C02: An equality, inequality, gap, anomaly coefficient, or residual is compared across inconsistent units, frames, or normalizations.
SCL-C03: Raw parent quantities, different chambers, different schemes, or different observable definitions are compared directly.
SCL-C04: A topology, ratio, or normalization convention is presented as creating an absolute physical unit.
SCL-C05: A measured/fixed radius, interval length, boundary position, temperature, or flux is used to assert that its fluctuation is absent or stabilized.
SCL-C06: “Compact,” “heavy,” “Planck suppressed,” or central-value separation is used without a quantitative physical gap.
SCL-C07: A physical stiffness is hidden as a constraint, or an exact multiplier is counted as a tunable physical parameter without justification.
SCL-C08: One candidate is called parameter-free by hiding discrete, global, boundary, normalization, or stiffness choices.
SCL-C09: Any constant contribution is omitted, double-counted, or cancelled across mismatched schemes without a protecting equation.
SCL-C10: A measured residual is called predicted, or a stability theorem is claimed to determine its observed magnitude.
SCL-C11: A static constant-term cancellation is promoted to compatibility with a finite phase transition or cosmological history.
SCL-C12: An isolated running coefficient, one-scale cancellation, or unmatched loop order is compared as a physical invariant.
SCL-C13: A quantity used to choose/fix the candidate is counted again as a successful prediction.
SCL-C14: A real coefficient is chosen after the anomaly is computed, or a factor-of-two/sign/quotient mismatch remains.
SCL-C15: Only central values or independent errors are compared, or a poorly identifiable output is declared uniquely derived.
SCL-C16: A small low-energy scale is called derived or natural solely because a parameter was chosen small or a cancellation occurs at one order.
SCL-C17: A zero-mode, finite tower, or finite heat-kernel prefix is promoted to an all-scale claim.
SCL-C18: A local temperature, horizon radius, correlation length, clock rate, or transition scale is treated as one global fixed ruler.
SCL-C19: A composite/effective mass or cutoff is treated as a new primitive anchor without provenance or while its constituents remain independently counted.
SCL-C20: Changing cutoff/resolution changes the claimed physical class without being detected, or noncommuting limits are silently exchanged.
SCL-C21: One convenient scale assignment or one successful matching route is treated as exhaustive without grammar or theorem.
SCL-C22: Simplicity, fewer dimensions, or cheaper computation is used to select a physically failing or distinguishable candidate.

Any authority, normalization, observation map, gate scope, boundary support, spectrum, threshold, regulator, or measurement-role change that affects a packet marks dependent certificates RESTART-REQUIRED.

16. Terminal

BB-SCL-4.0

DELIVERS:
  A complete, candidate-neutral, covariance-aware Scale object for gate execution,
  preserving BB-SCL-3.3 while adding hierarchy, tower/refinement, state-dependent,
  emergent-scale, uncertainty/identifiability, and exhaustion machinery.

STATUS:
  DEVELOPMENT AUTHORITY — MAXIMUM-RIGOR — NOT CANONICALLY RATIFIED.

Appendix A — `scalecertificatev3` exact compatibility schema

scale_certificate_v3:
  candidate_id:
  same_ruler_tuple:
  measured_anchors:
  calibration_inputs:
  derived_scales:
  radius_radion_ledger:
  compactification_gap:
  observation_window:
  field_and_bundle_normalizations:
  renormalization_scale:
  scheme_and_matching_order:
  cutoff_and_floor:
  constraint_multiplier_dimensions:
  physical_stiffness_parameters:
  determinant_contributions:
  cosmological_term_ledger:
  threshold_and_phase_transition_ledger:
  residual_lambda_owner:
  uncertainty_covariance:
  parameter_ledger:
  evidence_hashes:
  verdict:

Appendix B — Source preservation

Exact BB-SCL-3.3 SHA-256: 74b7d87ba07e1471dc0d3ed46b118721b8bd342b57fac3a130229553c851ab23
Exact source: 06SOURCES/BBSCL33EXACTARCHIVAL_SOURCE.md
Preservation map: 02REGISTRIES/LEGACYPRESERVATIONMATRIXV4_0.json

Appendix C — Exact BB-SCL-3.3 archival authority

The following is a read-only archival rendering. The byte-exact source remains in 06SOURCES/BBSCL33EXACTARCHIVAL_SOURCE.md and is hash-validated.

---
title: "BB-SCL-3.3 — Scale Provenance, Gaps, Vacuum, and Topological-Coefficient Ledger"
building_block_id: "BB-SCL-3.3"
version: "3.3"
date: "2026-07-24"
status: "DEVELOPMENT AUTHORITY — EVIDENCE-CRITERIA EXTENDED — NOT FROZEN"
scope: "Complete owned specification under package v3.3.2"
protocol_freeze: false
canonical_ratification: false
package_authority_version: "3.3.2"
---

# BB-SCL-3.3 — Scale Provenance, Gaps, Vacuum, and Topological-Coefficient Ledger

## 0. Purpose

Scale answers:

> **How do structural relations acquire physical magnitudes, which quantities are inputs or outputs, which fields fluctuate around those magnitudes, and how are candidates compared on one ruler without hiding vacuum terms or stabilization parameters?**

Scale enforces:

\[
\text{background value fixed}
\neq
\text{associated fluctuation absent},
\]

\[
\text{measured radius}
\neq
\text{radion stabilized},
\]

\[
\text{vacuum stability}
\neq
\text{vacuum value prediction}.
\]

## 1. Provenance classes

Every magnitude, coefficient, cutoff, radius, tolerance, and residual value receives exactly one class:

- `MEASURED-ANCHOR`;
- `CALIBRATION-INPUT`;
- `DERIVED-GIVEN-ANCHOR`;
- `THEOREM-DERIVED`;
- `STRUCTURAL-NORMALIZATION`;
- `CONSTRAINT-MULTIPLIER`;
- `PHYSICAL-COUPLING`;
- `GLOBAL-INTEGRATION-CONSTANT`;
- `BOUNDARY-DATUM`;
- `MATCHING-OUTPUT`;
- `SCHEME-DEPENDENT-INTERMEDIATE`;
- `MEASURED-RESIDUAL`;
- `FORBIDDEN-UNDECLARED`.

The class is frozen before comparison and may not change after a gate result.

## 2. Same-ruler tuple

Every comparison freezes

\[
\mathfrak R=
(D_{\rm parent},D_{\rm observer},\text{frame},\mu,\text{scheme},
\text{bundle norm},\text{field norm},\Pi,\Lambda_{\rm cutoff},
\Delta_0,\text{truncation},\text{observable definition}).
\]

A mismatch suspends comparison.

## 3. Structural versus absolute information

Shape may determine:

- topology;
- discrete multiplicities;
- group-theoretic ratios;
- dimensionless curvature ratios;
- index data.

It does not create an absolute unit.

A relation such as

\[
M_4^2=M_D^{D-2}V_{\rm int}
\]

requires declared values or derivations for the internal volume and one gravitational ruler.

## 4. Radius-versus-radion firewall

For every geometric scale \(R_a\), record separately:

1. background value \(R_a^{(0)}\);
2. whether \(R_a\) is a physical field;
3. kinetic normalization;
4. constraint or potential;
5. mass and mixing;
6. observer coupling;
7. evidence for absence or stabilization.

The required table is:

| Scale sector | Background provenance | Physical fluctuation? | Constraint or potential | Mass/gap | Status |
|---|---|---:|---|---:|---|
| Overall internal volume | | | | | |
| Relative factor radii | | | | | |
| Interval/radion length | | | | | |
| Bundle/Wilson-line scale | | | | | |
| Boundary position | | | | | |
| Compactification cutoff | | | | | |

A measured compactification scale does not remove a radion.

## 5. Quantitative compactification gap

For every nonzero physical internal mode retained in the candidate’s validity argument,

\[
m_{n}^{2}\ge M_{\rm gap}^{2}>E_{\rm obs}^{2}
\]

with a declared uncertainty margin.

The gap packet includes:

- lowest physical eigenvalue by sector;
- kinetic normalization;
- boundary conditions;
- mixing corrections;
- loop and matching order;
- cutoff and tail bound;
- comparison window.

“Compact” is not a decoupling certificate.

## 6. Constraint multiplier versus physical stiffness

An exact multiplier enforcing \(\Phi=0\) is not a tunable stabilizing mass.

A term

\[
\frac{\kappa}{2}\Phi^2
\]

contains a physical coupling \(\kappa\) and must be counted.

The limit \(\kappa\to\infty\) is not automatically equivalent to a constitutive restriction. The limiting measure, stress, determinant, and low-energy response must be shown.

## 7. Equal parameter accounting

For candidate \(i\), publish

\[
\mathcal P_i=
(N_{\rm measured},N_{\rm calibrated},N_{\rm physical},N_{\rm structural},
N_{\rm global},N_{\rm boundary},N_{\rm matching},N_{\rm constraints},N_{\rm discrete}).
\]

The same categories apply to every candidate.

A candidate is not parameter-free merely because its choices are discrete, global, boundary-localized, or embedded in a constraint definition.

## 8. Complete cosmological-term ledger

The renormalized four-dimensional constant term must be decomposed as

\[
\Lambda_{4,\rm ren}=
\Lambda_{\rm parent}
+\Lambda_{\rm internal\ curvature}
+\Lambda_{\rm flux}
+\Lambda_{\rm boundary}
+\Lambda_{\rm matter}
+\Lambda_{\rm constraint}
+\Lambda_{\det C}
+\Lambda_{\rm matching}
+\Lambda_{\rm graviton}
+\Lambda_{\rm residual}.
\]

Every term records:

- units and frame;
- renormalization scale;
- scheme;
- support;
- provenance type;
- dependence on internal geometry;
- dependence on thresholds;
- whether dynamically related to other terms;
- uncertainty;
- whether protected by a vacuum-offset identity;
- whether measured, calibrated, or predicted.

No cancellation between terms is credited unless enforced by a lawful parent, global, boundary, or symmetry equation.

## 9. Value-versus-stability firewall

### 9.1 Stability

Vacuum-offset stability asks whether

\[
\mathcal L_m\to\mathcal L_m-c
\]

changes local curvature observables.

### 9.2 Value

The present residual asks why

\[
\Lambda_{\rm residual}=\Lambda_{\rm obs}
\]

has its measured value.

Allowed value ownership is:

- theorem-derived;
- global integration constant fixed by independent boundary data;
- calibrated input;
- measured residual.

A stability theorem does not predict the residual. A measured residual does not establish stability.

## 10. Threshold and phase-transition ledger

For every heavy threshold or condensate transition, record:

- mass scale;
- before/after effective action;
- additive constant shift;
- nonconstant stress and latent heat;
- matching scheme;
- global or boundary response;
- cosmological history scope;
- residual effect.

Constant threshold cancellation may be exact while finite transition history remains nontrivial.

## 11. Scheme and renormalization transport

A scheme-dependent coefficient cannot be compared in isolation.

Under

\[
\mathbf c(\mu)\to\mathbf c'(\mu'),
\]

the complete observable and vacuum-response packet must be transported.

The same:

- loop order;
- threshold convention;
- regulator class;
- uncertainty policy;
- gravitational scope;

must be applied to every candidate.

## 12. Measured-anchor firewall

For every target quantity:

observablerole: observableid: role: measuredanchor|calibrationinput|derivedoutput|blindprediction|measuredresidual inputstage: candidate_dependence: uncertainty: transport:


A datum used to calibrate a candidate cannot be counted again as an independent prediction.

## 13. Economy and representative choice

Complexity and economy remain non-gating unless separately justified by a physical principle.

After one physical equivalence class survives, an economy vector may select a representative:

\[
\mathbf w_i=(D_i,N_{\rm measured},N_{\rm calibrated},N_{\rm physical},
N_{\rm discrete},L_{\rm description},C_{\rm computation}).
\]

No scalar exchange rate between these categories is assumed without an explicitly frozen ordering rule.

## 14. Scale certificate

scalecertificatev3: candidateid: samerulertuple: measuredanchors: calibrationinputs: derivedscales: radiusradionledger: compactificationgap: observationwindow: fieldandbundlenormalizations: renormalizationscale: schemeandmatchingorder: cutoffandfloor: constraintmultiplierdimensions: physicalstiffnessparameters: determinantcontributions: cosmologicaltermledger: thresholdandphasetransitionledger: residuallambdaowner: uncertaintycovariance: parameterledger: evidence_hashes: verdict:


## 15. Negative controls

### 15.1 Fixed radius with massless radion

Set \(R=R_0\) as a measured background but retain a flat radion potential.

Expected result: background scale anchored; stability fails.

### 15.2 Hidden stiffness

Use \(\kappa\Phi^2/2\) to stabilize a mode but count \(\kappa\) as a constraint multiplier.

Expected result: parameter-accounting failure.

### 15.3 Stable vacuum with measured residual

Use a valid constant-shift quotient but set the residual from observation.

Expected result: stability can pass; value is `MEASURED-RESIDUAL`, not predicted.

### 15.4 Accidental cancellation at one scale

Tune two scheme-dependent terms to cancel at \(\mu_0\) without a protecting equation.

Expected result: no radiative-stability credit.

## 16. Falsifiers and reopen triggers

This block fails or reopens if:

- a quantity lacks provenance;
- radius and radion are conflated;
- a physical stiffness is hidden as a constraint;
- a multiplier is counted as a tunable coupling without reason;
- compactification lacks a quantitative gap;
- different candidates use different rulers or uncertainty policies;
- a measured anchor is counted as a prediction;
- the cosmological ledger omits a term;
- a cancellation lacks a parent equation;
- stability and value are conflated;
- phase-transition history is inferred from static cancellation;
- scheme transport is incomplete.

## 17. Terminal

BB-SCL-3.3

DELIVERS: Same-ruler comparison, radius/radion separation, quantitative gaps, equal parameter accounting, and a complete vacuum-energy provenance ledger.

STATUS: DEVELOPMENT AUTHORITY CANDIDATE — NOT FROZEN.


## Integrated boundary/orbifold authority

This block is part of the **Candidate-Neutral Building-Block Authority v3.1 — Boundary and Inflow Development Candidate**.

The following rule is binding across the set:

> A bulk or quotient-space anomaly cancellation statement does not close a theory with orbifold fixed sets or physical boundaries. Each stratum requires a local anomaly ledger, and the complete quantum theory requires a relative/global trivialization compatible with gluing.

The dedicated owner is `BB-BND-1 — Orbifold Fixed-Set, Relative-Anomaly, and Inflow Completion`.

Every candidate containing a boundary, fixed set, defect, quotient singularity, interface, or parity projection must provide a `boundary_anomaly_completion_certificate`. Until that certificate passes:

- a chirality or no-mirror result is **CONDITIONAL-ON-BND**;
- quantum BRST/BV nilpotency is **CONDITIONAL-ON-BND**;
- a global-bordism result for the closed bulk target is not a complete boundary result;
- cancellation after integrating over the compact direction is not accepted as local gauge invariance;
- no gate may claim that the interval/orbifold construction is fully quantum consistent.

## Boundary/orbifold completion — topological and inflow coefficient provenance

### 1. Dimensionless does not mean unowned

Anomaly coefficients may be dimensionless and topological, but they still require provenance, normalization, and global quantization.

Each entry is typed as:

- representation-derived;
- index-derived;
- quantized topological coefficient;
- allowed local counterterm;
- measured input;
- forbidden tuned cancellation.

### 2. Inflow coefficient ledger

For every inflow term record:

inflowcoefficient: termid: differentialformnormalization: tracenormalization: globalgaugegroup: chargelattice: coefficient: quantizationlattice: largegaugetransformationtest: coveringtoquotientfactor: orientationconvention: derivedfromparent: counterterm_ambiguity: evidence:


A real coefficient chosen to cancel a computed anomaly is not a valid solution unless it belongs to the predeclared quantization lattice and is generated by an allowed parent term.

### 3. Same-ruler anomaly comparison

Bulk, boundary, and inflow anomaly coefficients must use the same:

- generator normalization;
- hypercharge normalization;
- global quotient;
- chirality convention;
- consistent/covariant current convention;
- fixed-set measure normalization.

A factor-of-two mismatch between covering and quotient descriptions is a gate failure, not a harmless convention.

### 4. Metric independence and vacuum interactions

A purely topological inflow term may be metric-independent, but:

- boundary counterterms can carry stress;
- regulator determinants can contribute to vacuum matching;
- top forms can be shared with vacuum-sequestering sectors.

Therefore a boundary-anomaly repair must update the Vacuum ledger whenever it changes a metric-dependent term, flux sector, boundary tension, or global integration constant.

### 5. Scale falsifiers

Scale fails if:

- a Chern–Simons coefficient is unquantized;
- trace normalizations differ across the ledger;
- a quotient factor is omitted;
- a counterterm coefficient is fitted after comparison;
- an anomaly repair silently changes the vacuum ledger.

# Block-Specific Standalone Interface — Scale and Provenance

## Owned questions

This block alone owns:

- same-ruler comparison;
- measured/calibrated/derived provenance;
- compactification gaps and uncertainty transport;
- radius-versus-radion distinction;
- parameter and discrete-choice accounting;
- complete cosmological-term ledger;
- inflow/topological coefficient normalization and quantization;
- renormalization and matching transport.

## Required outputs

- same-ruler tuple;
- complete parameter/provenance ledger;
- quantitative gap certificate;
- vacuum-term decomposition;
- measured-anchor firewall;
- topological/inflow coefficient ledger;
- scheme and uncertainty packet.

## Non-ownership boundary

Scale does not prove:

- a modulus is absent merely because a background radius is fixed;
- vacuum stability merely because the residual value is measured;
- inflow consistency merely because a coefficient is dimensionless;
- physical selection merely because one branch is economically simpler.

# Complete Reconstruction Procedure — Scale and Provenance

## 1. Universal provenance assignment

Every number, coefficient, discrete choice, normalization, and tolerance must appear in a single provenance table.

Required columns:

| Field | Required content |
|---|---|
| object ID | stable identifier |
| symbol/value | exact or numerical value |
| units | including dimensionless |
| provenance type | measured, calibrated, derived, structural, multiplier, physical coupling, matching, scheme-dependent, forbidden |
| owner | block and parent term |
| scale/frame | renormalization scale and frame |
| normalization | trace, field, bundle, and quotient conventions |
| uncertainty | covariance or exact status |
| dependence | upstream objects |
| role | input, output, negative control, or diagnostic |

A dimensionless number is not automatically structural. A topological coefficient still requires a quantization lattice. A discrete choice is still an input unless derived.

## 2. Same-ruler reconstruction

Before comparing two candidates, align:

\[
(
D_{\rm parent},
D_{\rm observer},
\text{frame},
\mu,
\text{scheme},
\text{field normalization},
\text{bundle normalization},
\text{global quotient},
\Pi,
\Lambda_{\rm cutoff},
\text{observable}
).
\]

The reconstruction report must show every transport step. A raw higher-dimensional coefficient cannot be compared directly with a projected four-dimensional observable.

## 3. Scale-versus-field checklist

For each radius or scale, separately answer:

1. What fixes the background value?
2. Is there a physical fluctuation?
3. What is its kinetic normalization?
4. Is it gauge, constrained, massive, massless, tachyonic, or external?
5. What is the physical gap?
6. Which equation fixes or measures it?

This prevents “radius measured” from becoming “radion absent.”

## 4. Complete vacuum ledger

The four-dimensional constant term must be reconstructed as a sum of typed contributions:

\[
\Lambda_{4,\rm eff}
=
\Lambda_{\rm parent}
+\Lambda_{\rm curvature}
+\Lambda_{\rm matter}
+\Lambda_{\rm boundary}
+\Lambda_{\rm flux}
+\Lambda_{\rm determinant}
+\Lambda_{\rm matching}
+\Lambda_{\rm residual}.
\]

For every term record:

- sign;
- units;
- frame;
- scale;
- scheme;
- metric dependence;
- threshold dependence;
- whether varied;
- whether protected under constant shifts;
- whether it changes during phase transitions;
- whether it is derived, calibrated, measured, or open.

An apparent numerical cancellation at one scale is not a stability theorem.

## 5. Inflow and topological coefficient reconstruction

For every anomaly-inflow coefficient, verify:

- differential-form convention;
- trace normalization;
- actual global gauge group;
- charge lattice;
- quotient normalization;
- coefficient lattice;
- large-gauge transformation;
- fixed-set orientation signs;
- counterterm ambiguity;
- parent provenance.

A coefficient that happens to cancel a local anomaly but fails quantization is rejected.

## 6. Economy firewall

Any economy comparison is reported as a vector until an ordering rule is frozen.

No scalar cost can silently exchange:

- one dimension;
- one measured real;
- one calibrated real;
- one discrete quotient;
- one new Actor;
- one boundary term;
- one theorem assumption.

Economy cannot rescue a hard physics failure and cannot establish physical uniqueness among operationally equivalent candidates.

## 7. Final reconstruction test

A fresh agent must be able to:

- change the renormalization scheme and transport the full coupled prediction;
- reclassify a fitted stiffness as a physical coupling;
- distinguish a measured residual from vacuum stability;
- detect an omitted quotient factor in an inflow coefficient;
- detect a massless radion despite a fixed radius.

If any test is impossible from the file and its certificate schema, the Scale block is incomplete.

## Observer ruler ownership

Scale owns units, frames, renormalization schemes, and transport equations. OBS owns the actual parent-to-record map. A same-ruler PASS requires both certificates and a shared ruler-tuple hash.

No scale or normalization may be selected after a target residual is inspected.

## Owned hard constraints and acceptance evidence

The full controlling registry is `EVIDENCE_DISCHARGE_REGISTRY_V3_3_2.md`. The rows below are embedded because this block owns or directly co-owns them.

| ID | Required witness | Minimal discharge | Fail trigger |
|---|---|---|---|
| `GEN-C02` | Layer/provenance ledger + uniqueness check | A ledger assigns exactly one primary layer and provenance class to every load-bearing object; a script reports no duplicates or unowned rows. | An object changes layer after comparison or has no primary provenance. |
| `GEN-C04` | Observer-map certificate + same-ruler transport output | A frozen map sends the parent state to the measured record with dimension, frame, scheme, scale, bundle norm, and projection shown; the wrong-ruler control fails as designed. | A raw parent quantity is compared directly with a differently normalized record. |
| `GEN-C09` | Gap calculation + uncertainty covariance + ruler packet | The lightest omitted physical mode exceeds the observation window by the frozen margin after uncertainty propagation. | The claimed gap is qualitative, uses a different normalization, or closes only at central values. |
| `VAC-C03` | Renormalized vacuum-term decomposition | Every contribution to \(\Lambda_{4,
m eff}\) is listed with sign, units, frame, scheme, threshold dependence, and owner. | A cancellation combines untyped terms or omits determinant/boundary contributions. |
| `VAC-C07` | Loop/threshold scope ledger | Matter, graviton, boundary, constraint determinant, matching, and threshold contributions are separately marked included, excluded, or open. | A matter-only proof is presented as full quantum stability. |
| `VAC-C08` | Residual-value ownership certificate | The observed residual is explicitly derived, globally/boundary fixed, calibrated, measured, or left OPEN—exactly one owner. | A measured residual is presented as a prediction or appears twice in the ledger. |
| `BND-C02` | Cover/quotient conversion table | Volume factors, delta normalizations, parity traces, orientation signs, and gauge restrictions agree between the cover and quotient descriptions. | An unexplained factor of two or sign discrepancy remains. |
| `BND-C06` | Quantized inflow/counterterm certificate | The parent inflow action, coefficient lattice, large-gauge test, orientations, and pre-freeze provenance are published. | A fitted real coefficient cancels the residual but is not globally quantized. |
| `OBS-C04` | Frozen ruler-tuple comparison | Dimension, frame, renormalization scale, scheme, bundle norm, chamber projection, truncation, regulator, and observable definition are identical or explicitly transported. | A 13D norm is compared directly with a one-chamber 4D running observable. |
| `OBS-C08` | Full covariance and scheme-transport output | Uncertainties and correlations are propagated through the map, including scheme/frame transformations and truncation error. | Only central values or independent errors are compared. |

## Package status and authority boundary

This file belongs to the **Candidate-Neutral Building-Block Authority v3.3.2**.

The package is documentation-complete for the current development architecture, but it is not protocol-frozen and not canonically ratified. Technical results generated under it remain development evidence until the control suite, enumeration test, and hostile review pass.

The controlling package authorities are:

- `EVIDENCE_DISCHARGE_REGISTRY_V3_3_2.md`;
- `QUANTITATIVE_STOPPING_AND_EXHAUSTION_RULE_V3_3_2.md`;
- `MANDATORY_CONTROL_SUITE_V3_3_2.md`;
- `MIGRATION_AND_SUPERSESSION_RECORD_V3_3.md`.

A block is standalone for its owned object: it includes its complete definitions, interfaces, certificates, falsifiers, and owned evidence criteria. The full cross-block registry is intentionally stored once rather than repeated verbatim in every block.

### Shared status grammar

PASS: The named witness satisfies the minimal discharge criterion.

FAIL: A reproducible counterexample or failed acceptance test exists.

OPEN: The required witness is missing, incomplete, or inconclusive.

NOT-EVALUATED: Evaluation stopped after an earlier hard failure.

NOT-APPLICABLE: A type proof establishes that the requirement cannot apply.

CONSTRUCTION-ANCHOR: A declared Actor, constraint, boundary term, or global sector realizes the result but does not derive it from the pre-existing object.

CONDITIONAL-ON-BND-A: The spectrum/domain result awaits fixed-set and operator-domain closure.

CONDITIONAL-ON-BND-B: The quantum result awaits local and global anomaly/inflow closure.

RESTART-REQUIRED: A frozen object relevant to the result changed.


### Universal anti-promotion rules

- A bare candidate is not a complete parent object.
- A definition is not a witness.
- A nonempty equation list is not a solvability proof.
- An isolated vacuum is not automatically stable.
- A fixed background value is not automatically an absent fluctuation.
- Static vacuum-offset protection is not automatically cosmological-history compatibility.
- Integrated anomaly cancellation is not local fixed-set cancellation.
- Local anomaly cancellation is not global determinant-line trivialization.
- A raw higher-dimensional quantity is not automatically the measured four-dimensional observable.
- One tested survivor is not a selected survivor without explicit grammar enumeration or a finiteness theorem.

02_REGISTRIES

Machine-readable constraints and gate crosswalks.

LEGACY_PRESERVATION_MATRIX_V4_1.json789 bytes

scale/02_REGISTRIES/LEGACY_PRESERVATION_MATRIX_V4_1.json

{
  "schema": "scale-preservation-matrix-v4.1",
  "date": "2026-08-02",
  "sources": [
    {
      "source": "BB-SCL-3.3",
      "path": "06_SOURCES/BB_SCL_3_3_EXACT_ARCHIVAL_SOURCE.md",
      "sha256": "74b7d87ba07e1471dc0d3ed46b118721b8bd342b57fac3a130229553c851ab23",
      "status": "EXACT"
    },
    {
      "source": "BB-SCL-4.0 core",
      "path": "06_SOURCES/BB_SCL_4_0_EXACT_ARCHIVAL_SOURCE.md",
      "sha256": "c248db18ad92dac0dd0dcee9f23c0c6e4adb0f7b3731c34432f3c1160c97348e",
      "status": "EXACT"
    },
    {
      "source": "BB-SCL-4.0 package",
      "path": "06_SOURCES/PREVIOUS_BB_SCL_4_0_PACKAGE",
      "status": "EXACT-DIRECTORY-COPY"
    }
  ],
  "new_constraints": [
    "SCL-C23",
    "SCL-C24",
    "SCL-C25",
    "SCL-C26"
  ],
  "weakened_legacy_rows": 0
}

SCALE_CONSTRAINT_REGISTRY_V4_1.csv9,432 bytes

scale/02_REGISTRIES/SCALE_CONSTRAINT_REGISTRY_V4_1.csv

id,name,old,question,outputs,primary_owner,coowners
SCL-C01,Universal scale provenance and unique ownership,True,"Does every magnitude, coefficient, cutoff, tolerance, normalization, discrete scale choice, and residual have exactly one frozen provenance class and one primary owner?",provenance_ledger|dependency_hashes,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C02,"Dimensional, unit, frame, and normalization closure",True,Are every equation and comparison dimensionally closed in one declared frame and normalization system?,dimensional_closure_packet|same_ruler_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C03,Same-ruler comparison and Observer transport,True,Are all candidates and records compared using the same frozen ruler tuple and the same Observer map?,same_ruler_packet|uncertainty_covariance_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C04,Structural information versus absolute scale and anchor identifiability,True,Does the derivation distinguish dimensionless structural relations from the independent anchors required to assign absolute magnitudes?,anchor_identifiability_packet|provenance_ledger,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C05,Background scale versus physical fluctuation,True,"For every geometric or environmental scale, is the background value separated from its physical fluctuation, kinetic normalization, potential, mass, mixing, and Observer coupling?",radius_radion_ledger|gap_decoupling_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C06,"Quantitative gaps, decoupling, and observation windows",True,"Is every omitted physical mode quantitatively separated from the claimed observation window after normalization, mixing, uncertainty, and boundary effects?",gap_decoupling_packet|tower_matching_tail_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C07,Constraint multiplier versus physical stiffness,True,"Are exact multipliers, constitutive restrictions, penalties, and physical stabilizing couplings kept distinct?",multiplier_stiffness_packet|parameter_accounting_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C08,"Equal parameter, discrete-choice, boundary, and global accounting",True,"Are all candidates charged with the same categories of measured, calibrated, physical, structural, global, boundary, matching, constraint, and discrete inputs?",parameter_accounting_packet|economy_vector_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C09,Complete vacuum and cosmological-term ledger,True,"Are all contributions to the renormalized constant term represented on one scale, frame, scheme, and support ledger?",vacuum_term_ledger|scheme_rg_matching_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C10,Vacuum stability versus residual-value ownership,True,Are invariance under constant matter shifts and the numerical ownership of the observed residual treated as separate claims?,vacuum_stability_value_packet|measured_anchor_firewall_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C11,"Threshold, phase-transition, and history scale ledger",True,Are heavy thresholds and finite transitions tracked through both static matching and time-dependent history?,threshold_phase_history_packet|state_dependent_scale_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C12,"Renormalization, scheme, RG, and matching transport",True,Are scheme-dependent coefficients transported only as part of a complete coupled observable packet?,scheme_rg_matching_packet|uncertainty_covariance_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C13,"Measured-anchor, calibration, prediction, and residual firewall",True,"Is every datum assigned exactly one inferential role, with no training-on-the-test or double counting?",measured_anchor_firewall_packet|provenance_ledger,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C14,Topological and inflow coefficient normalization and quantization,True,"Are dimensionless topological coefficients globally normalized, quantized, and pre-owned rather than tuned?",topological_coefficient_packet|same_ruler_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C15,"Uncertainty covariance, sensitivity, and identifiability",False,"Are uncertainties, correlations, parameter sensitivities, degeneracies, and truncation errors propagated through the full map?",uncertainty_covariance_packet|anchor_identifiability_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C16,"Hierarchy, naturalness, and radiative-sensitivity diagnosis",False,"Are large scale separations classified by actual protection, sensitivity, and matching structure rather than aesthetic labels?",hierarchy_sensitivity_packet|scheme_rg_matching_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C17,"Multi-scale EFT, tower matching, truncation, and tail control",False,Does every finite-mode or finite-operator calculation state its scale interval and control omitted towers/tails?,tower_matching_tail_packet|resolution_refinement_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C18,"Time, temperature, horizon, correlation, and state-dependent scales",False,"Are scales that depend on state, history, region, horizon, temperature, or synchronization treated as derived fields/records rather than fixed universal constants?",state_dependent_scale_packet|same_ruler_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C19,"Composite, emergent, and effective scale provenance",False,"Are bound-state masses, condensate scales, correlation lengths, soliton sizes, and emergent effective cutoffs derived from constituent dynamics rather than silently promoted to primitive inputs?",emergent_scale_packet|parameter_accounting_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C20,Resolution and refinement lattice consistency with Granularity,False,"Do scale cutoffs, observational resolution, discretization, and Granularity classes form a monotone refinement system?",resolution_refinement_packet|tower_matching_tail_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C21,"Candidate-neutral scale grammar, saturation, and exhaustion",False,"Has every scale-bearing object, anchor choice, matching scale, cutoff, threshold, normalization, and admissible scale route been generated and given a disposition?",scale_grammar_exhaustion_packet|residual_vector_packet,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C22,Economy and representative-selection firewall,True,"Is economy used only after physical equivalence and without an undeclared exchange rate among dimensions, parameters, computations, and assumptions?",economy_vector_packet|gate_scale_summary,Scale,Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed
SCL-C23,"Scale-transformation covariance, homogeneity, and anomalous dimensions",False,"Does every scale-bearing field, operator, observable, spectrum, and response come with its transformation law under a change of physical scale, rather than only a value at one reference point?",scale_transformation_packet,Scale,Dynamics|Observer|Shape|Granularity as typed
SCL-C24,"Scale-symmetry breaking, trace/Weyl anomaly, and dimensional transmutation",False,"Are explicit, spontaneous, and anomalous breaking of scale symmetry separated, and are dynamically generated invariant scales derived rather than silently inserted as primitive anchors?",scale_anomaly_transmutation_packet|emergent_scale_packet|scheme_rg_matching_packet,Scale,Dynamics|Vacuum|Boundary|Observer as typed
SCL-C25,"Criticality, universality, finite-size scaling, and crossover",False,"Are claims near fixed points, phase transitions, continuum limits, or thermodynamic limits supported by critical exponents, universality data, finite-size scaling, and crossover control?",critical_scaling_universality_packet|resolution_refinement_packet|state_dependent_scale_packet,Scale,Dynamics|Boundary|Granularity|Rigidity|Vacuum as typed
SCL-C26,"Extensive, intensive, area/volume/fractal scaling, and regional composition",False,"Do regional, thermodynamic, entropic, geometric, and information quantities obey the correct scaling and composition law across changes of region size and shape?",composition_scaling_packet|state_dependent_scale_packet|resolution_refinement_packet,Scale,Boundary|Observer|Dynamics|Granularity as typed

SCALE_CONSTRAINT_REGISTRY_V4_1.json44,306 bytes

scale/02_REGISTRIES/SCALE_CONSTRAINT_REGISTRY_V4_1.json

{
  "schema": "scale-constraint-registry-v4.1",
  "date": "2026-08-02",
  "constraints": [
    {
      "id": "SCL-C01",
      "name": "Universal scale provenance and unique ownership",
      "question": "Does every magnitude, coefficient, cutoff, tolerance, normalization, discrete scale choice, and residual have exactly one frozen provenance class and one primary owner?",
      "formal": "For the scale-object universe $\\mathcal U_{\\rm scl}$, require a total typed map\n\\[\n\\operatorname{prov}:\\mathcal U_{\\rm scl}\\rightarrow\\mathcal P_{\\rm allowed},\n\\qquad\n\\operatorname{owner}:\\mathcal U_{\\rm scl}\\rightarrow\\mathcal B,\n\\]\nwith exactly one primary value for each map.  Provenance may be refined by secondary dependencies but may not be changed after a gate result is inspected.",
      "inputs": [
        "all numerical and discrete objects",
        "parent-term ledger",
        "calibration and measurement manifest",
        "gate freeze hash"
      ],
      "algorithm": [
        "enumerate every load-bearing scalar, tensor coefficient, scale and tolerance",
        "assign one allowed provenance class",
        "assign one primary block/parent-term owner",
        "run duplicate, orphan, and post-target mutation tests"
      ],
      "outputs": [
        "provenance_ledger",
        "dependency_hashes"
      ],
      "witness": "Complete machine-readable provenance table with zero orphan, duplicate-primary, or post-freeze mutation rows.",
      "fail": "Any load-bearing quantity is unowned, multiply primary-owned, retrospectively reclassified, or supplied only by the desired gate result.",
      "control": "Insert a dimensionless coefficient with no owner; the validator must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C02",
      "name": "Dimensional, unit, frame, and normalization closure",
      "question": "Are every equation and comparison dimensionally closed in one declared frame and normalization system?",
      "formal": "Every asserted equality $X=Y$ requires\n\\[\n[ X ]=[ Y ],\\quad F_X=F_Y,\\quad N_X=N_Y,\n\\]\nwhere $[\\cdot]$ is the unit/dimension vector, $F$ the physical frame, and $N$ the complete field, trace, bundle, quotient, and measure normalization packet.",
      "inputs": [
        "equation vector",
        "unit basis",
        "frame map",
        "normalization ledgers"
      ],
      "algorithm": [
        "construct dimension vectors for every term",
        "transport all terms to a frozen frame",
        "apply trace/bundle/field/quotient normalization maps",
        "reject unmatched or implicit conversion factors"
      ],
      "outputs": [
        "dimensional_closure_packet",
        "same_ruler_packet"
      ],
      "witness": "Symbolic dimensional audit plus explicit frame and normalization transforms for every compared quantity.",
      "fail": "An equality, inequality, gap, anomaly coefficient, or residual is compared across inconsistent units, frames, or normalizations.",
      "control": "Compare a 13D coefficient directly to a 4D canonically normalized observable; the audit must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C03",
      "name": "Same-ruler comparison and Observer transport",
      "question": "Are all candidates and records compared using the same frozen ruler tuple and the same Observer map?",
      "formal": "Freeze\n\\[\n\\mathfrak R=(D_{\\rm parent},D_{\\rm obs},F,\\mu,{\\cal S},N_{\\rm bundle},N_{\\rm field},G_{\\rm global},\\Pi,\\Lambda,\\Delta,\\mathcal T,\\mathcal O).\n\\]\nComparison is admissible only when the tuples are identical or a complete invertible/controlled transport is supplied.",
      "inputs": [
        "candidate ruler tuples",
        "Observer certificate",
        "scheme/frame transports",
        "observable definitions"
      ],
      "algorithm": [
        "hash each ruler tuple",
        "align dimensions, frames, scale, scheme and normalizations",
        "transport covariance and truncation errors",
        "run wrong-ruler negative control"
      ],
      "outputs": [
        "same_ruler_packet",
        "uncertainty_covariance_packet"
      ],
      "witness": "Shared ruler hash or explicit transport chain with uncertainty propagation and inverse/consistency check.",
      "fail": "Raw parent quantities, different chambers, different schemes, or different observable definitions are compared directly.",
      "control": "Use a one-chamber 4D running mass against an unprojected higher-dimensional norm; the audit must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C04",
      "name": "Structural information versus absolute scale and anchor identifiability",
      "question": "Does the derivation distinguish dimensionless structural relations from the independent anchors required to assign absolute magnitudes?",
      "formal": "If Shape fixes a relation $f(x_1,\\ldots,x_n)=0$, Scale must compute the rank of the scale-identification map.  Absolute prediction requires the number of independent anchors to equal the unresolved dimensional rank and the inverse map to be identifiable.",
      "inputs": [
        "structural relations",
        "dimension matrix",
        "anchor list",
        "Jacobian of observable map"
      ],
      "algorithm": [
        "separate dimensionless and dimensionful relations",
        "compute rank/nullity of the dimension matrix",
        "identify the minimal anchor set",
        "test local/global identifiability and degeneracy"
      ],
      "outputs": [
        "anchor_identifiability_packet",
        "provenance_ledger"
      ],
      "witness": "Rank calculation showing exactly which absolute magnitudes are derived and which remain measured/calibrated/global inputs.",
      "fail": "A topology, ratio, or normalization convention is presented as creating an absolute physical unit.",
      "control": "Give all dimensionless ratios but no independent mass/length anchor; absolute masses must remain OPEN.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C05",
      "name": "Background scale versus physical fluctuation",
      "question": "For every geometric or environmental scale, is the background value separated from its physical fluctuation, kinetic normalization, potential, mass, mixing, and Observer coupling?",
      "formal": "For each scale $R_a$, publish\n\\[\nR_a=R_a^{(0)}+Z_a^{-1/2}\\,\\delta R_a\n\\]\nand classify $\\delta R_a$ as gauge, constrained, external, massive, massless, tachyonic, or absent by a type theorem.",
      "inputs": [
        "Shape deformation basis",
        "Dynamics Hessian",
        "Rigidity certificate",
        "Observer coupling map"
      ],
      "algorithm": [
        "enumerate all scale-bearing backgrounds",
        "construct fluctuation variables and kinetic form",
        "apply constraints/gauge quotient",
        "compute mass/mixing and response",
        "require type proof for absence"
      ],
      "outputs": [
        "radius_radion_ledger",
        "gap_decoupling_packet"
      ],
      "witness": "Complete background/fluctuation ledger with operator, domain, mass/gap, mixing, and response evidence.",
      "fail": "A measured/fixed radius, interval length, boundary position, temperature, or flux is used to assert that its fluctuation is absent or stabilized.",
      "control": "Fix a radius numerically while retaining a flat radion potential; stability must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C06",
      "name": "Quantitative gaps, decoupling, and observation windows",
      "question": "Is every omitted physical mode quantitatively separated from the claimed observation window after normalization, mixing, uncertainty, and boundary effects?",
      "formal": "For every omitted sector $n$ require\n\\[\nm_{n,\\rm phys}^2-E_{\\rm max}^2 \\ge M_{\\rm margin}^2>0\n\\]\nwith covariance, mixing, loop/matching order, domain, and tail scope included.",
      "inputs": [
        "physical spectrum",
        "boundary domains",
        "mixing matrices",
        "observation window",
        "uncertainty covariance"
      ],
      "algorithm": [
        "identify the lightest omitted physical eigenvalue per sector",
        "canonically normalize and diagonalize",
        "propagate covariance and truncation error",
        "compare worst-case lower bound to the observation window",
        "certify tail or limit scope"
      ],
      "outputs": [
        "gap_decoupling_packet",
        "tower_matching_tail_packet"
      ],
      "witness": "Sector-by-sector lowest-mode table and robust uncertainty-margin calculation.",
      "fail": "“Compact,” “heavy,” “Planck suppressed,” or central-value separation is used without a quantitative physical gap.",
      "control": "Choose a central gap above the cutoff whose lower confidence bound enters the window; closure must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C07",
      "name": "Constraint multiplier versus physical stiffness",
      "question": "Are exact multipliers, constitutive restrictions, penalties, and physical stabilizing couplings kept distinct?",
      "formal": "A multiplier term $\\lambda\\Phi$ and a stiffness term $\\kappa\\Phi^2/2$ belong to different measure and response classes.  A limiting claim $\\kappa\\to\\infty$ requires convergence of the measure, stress, determinants, spectrum, and low-energy observables.",
      "inputs": [
        "parent action",
        "constraint classification",
        "measure/determinant packet",
        "response functions"
      ],
      "algorithm": [
        "classify each enforcing term",
        "compute whether its coefficient fluctuates or runs",
        "compare finite-stiffness and exact-constraint measures",
        "test limiting convergence and residual stress"
      ],
      "outputs": [
        "multiplier_stiffness_packet",
        "parameter_accounting_packet"
      ],
      "witness": "Term-by-term classification with dimensionality, physical status, measure contribution, and limiting proof where invoked.",
      "fail": "A physical stiffness is hidden as a constraint, or an exact multiplier is counted as a tunable physical parameter without justification.",
      "control": "Stabilize a mode with $\\kappa\\Phi^2/2$ but label $\\kappa$ a multiplier; the audit must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C08",
      "name": "Equal parameter, discrete-choice, boundary, and global accounting",
      "question": "Are all candidates charged with the same categories of measured, calibrated, physical, structural, global, boundary, matching, constraint, and discrete inputs?",
      "formal": "Publish for candidate $i$\n\\[\n\\mathcal P_i=(N_m,N_c,N_p,N_s,N_g,N_b,N_{\\rm match},N_{\\rm con},N_d)\n\\]\nplus the full object list.  No category may be omitted because its values are discrete, topological, global, boundary-localized, or hidden in a definition.",
      "inputs": [
        "candidate manifests",
        "provenance ledger",
        "boundary/global data",
        "matching packets"
      ],
      "algorithm": [
        "enumerate all independent choices",
        "classify each choice identically across candidates",
        "detect aliases and hidden inputs",
        "compare vectors without an undeclared scalar exchange rate"
      ],
      "outputs": [
        "parameter_accounting_packet",
        "economy_vector_packet"
      ],
      "witness": "Equal-category parameter tables and machine check reporting no omitted or differently classified candidate input.",
      "fail": "One candidate is called parameter-free by hiding discrete, global, boundary, normalization, or stiffness choices.",
      "control": "Move a fitted real parameter into a boundary datum and claim improved economy; the comparison must reject it.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C09",
      "name": "Complete vacuum and cosmological-term ledger",
      "question": "Are all contributions to the renormalized constant term represented on one scale, frame, scheme, and support ledger?",
      "formal": "Require\n\\[\n\\Lambda_{4,\\rm ren}=\\Lambda_{\\rm parent}+\\Lambda_{\\rm curv}+\\Lambda_{\\rm flux}+\\Lambda_{\\rm bnd}+\\Lambda_{\\rm matter}+\\Lambda_{\\rm con}+\\Lambda_{\\det}+\\Lambda_{\\rm match}+\\Lambda_{\\rm grav}+\\Lambda_{\\rm residual},\n\\]\nwith every term typed, varied where appropriate, and transported consistently.",
      "inputs": [
        "parent/effective actions",
        "determinants",
        "boundary terms",
        "thresholds",
        "Vacuum certificate"
      ],
      "algorithm": [
        "enumerate all constant terms by support and owner",
        "transport to one frame/scheme/scale",
        "record metric dependence and variation status",
        "include threshold, determinant, graviton and matching terms",
        "test protected versus accidental cancellations"
      ],
      "outputs": [
        "vacuum_term_ledger",
        "scheme_rg_matching_packet"
      ],
      "witness": "Complete signed ledger with units, frame, scale, scheme, support, owner, threshold dependence, uncertainty, and protection status.",
      "fail": "Any constant contribution is omitted, double-counted, or cancelled across mismatched schemes without a protecting equation.",
      "control": "Omit the constraint determinant contribution while claiming a complete vacuum cancellation; the audit must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C10",
      "name": "Vacuum stability versus residual-value ownership",
      "question": "Are invariance under constant matter shifts and the numerical ownership of the observed residual treated as separate claims?",
      "formal": "The stability test is\n\\[\n\\mathcal L_m\\mapsto\\mathcal L_m-c\\quad\\Rightarrow\\quad \\delta \\mathcal O_{\\rm local}=0,\n\\]\nwhile value ownership requires exactly one of theorem-derived, independently boundary/global fixed, calibrated input, measured residual, or OPEN.",
      "inputs": [
        "Vacuum response law",
        "residual value source",
        "boundary/global equations",
        "measurement ledger"
      ],
      "algorithm": [
        "execute constant-shift response test",
        "trace residual value provenance independently",
        "reject double ownership",
        "state separate terminals for stability and value"
      ],
      "outputs": [
        "vacuum_stability_value_packet",
        "measured_anchor_firewall_packet"
      ],
      "witness": "Two independent certificates: constant-shift response and single-owner residual-value classification.",
      "fail": "A measured residual is called predicted, or a stability theorem is claimed to determine its observed magnitude.",
      "control": "Use exact shift protection but insert the residual from observation; stability may pass while prediction must not.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C11",
      "name": "Threshold, phase-transition, and history scale ledger",
      "question": "Are heavy thresholds and finite transitions tracked through both static matching and time-dependent history?",
      "formal": "For each transition $\\alpha$ publish before/after effective actions, matching map, additive shift, latent heat, nonconstant stress, transition duration, temperature/time scale, and residual history effect.",
      "inputs": [
        "Dynamics history packet",
        "Vacuum history packet",
        "threshold spectra",
        "thermal/phase data"
      ],
      "algorithm": [
        "enumerate every threshold and condensate transition",
        "derive before/after actions",
        "compute matching and additive shifts",
        "track finite-time stress and global/boundary response",
        "propagate to later observables"
      ],
      "outputs": [
        "threshold_phase_history_packet",
        "state_dependent_scale_packet"
      ],
      "witness": "Complete chronological threshold/phase ledger with static and dynamical effects separately evaluated.",
      "fail": "A static constant-term cancellation is promoted to compatibility with a finite phase transition or cosmological history.",
      "control": "Cancel constants before and after a transition but retain nonzero latent heat; history must remain nontrivial.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C12",
      "name": "Renormalization, scheme, RG, and matching transport",
      "question": "Are scheme-dependent coefficients transported only as part of a complete coupled observable packet?",
      "formal": "Under $(\\mathbf c,\\mu,{\\cal S})\\mapsto(\\mathbf c',\\mu',{\\cal S}')$, require a transport map for the full effective action/observable vector and covariance, with matching-order and threshold conventions frozen.",
      "inputs": [
        "beta functions",
        "matching maps",
        "scheme transformations",
        "observable vector",
        "covariance"
      ],
      "algorithm": [
        "freeze loop and truncation order",
        "transport the coupled coefficient vector",
        "include operator mixing and thresholds",
        "propagate covariance and truncation error",
        "check physical observable invariance within declared scope"
      ],
      "outputs": [
        "scheme_rg_matching_packet",
        "uncertainty_covariance_packet"
      ],
      "witness": "Coupled transport calculation showing scheme/frame dependence cancels or is explicitly retained in the physical prediction.",
      "fail": "An isolated running coefficient, one-scale cancellation, or unmatched loop order is compared as a physical invariant.",
      "control": "Tune two terms to cancel at one renormalization scale with no protecting equation; no stability credit is allowed.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C13",
      "name": "Measured-anchor, calibration, prediction, and residual firewall",
      "question": "Is every datum assigned exactly one inferential role, with no training-on-the-test or double counting?",
      "formal": "Each observable receives one role in\n\\[\n\\{\\text{measured anchor},\\text{calibration input},\\text{derived output},\\text{blind prediction},\\text{measured residual}\\}.\n\\]\nA datum may change role only under a new predeclared experiment and freeze.",
      "inputs": [
        "observable manifest",
        "fit/calibration history",
        "candidate dependence",
        "uncertainty"
      ],
      "algorithm": [
        "assign one role per observable",
        "record the stage at which it enters",
        "trace candidate dependence",
        "exclude calibrated observables from independent prediction counts",
        "run role-duplication test"
      ],
      "outputs": [
        "measured_anchor_firewall_packet",
        "provenance_ledger"
      ],
      "witness": "Role ledger with zero duplicates and an independent prediction set disjoint from calibration inputs.",
      "fail": "A quantity used to choose/fix the candidate is counted again as a successful prediction.",
      "control": "Fit a mass and then count the same mass as a blind prediction; the audit must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C14",
      "name": "Topological and inflow coefficient normalization and quantization",
      "question": "Are dimensionless topological coefficients globally normalized, quantized, and pre-owned rather than tuned?",
      "formal": "For coefficient $k$, require $k\\in\\Lambda_{\\rm quant}$ under the declared differential-form, trace, charge-lattice, global-group, quotient, and orientation conventions, and pass all large-gauge tests.",
      "inputs": [
        "Boundary anomaly/inflow packet",
        "global gauge group",
        "charge lattice",
        "trace/form conventions"
      ],
      "algorithm": [
        "construct the quantization lattice",
        "transport cover/quotient and orientation factors",
        "test large transformations",
        "classify counterterm ambiguity",
        "verify parent provenance before residual inspection"
      ],
      "outputs": [
        "topological_coefficient_packet",
        "same_ruler_packet"
      ],
      "witness": "Exact coefficient-lattice and large-gauge certificate sharing normalization hashes with Boundary.",
      "fail": "A real coefficient is chosen after the anomaly is computed, or a factor-of-two/sign/quotient mismatch remains.",
      "control": "Choose an unquantized Chern–Simons coefficient that cancels the local residual; global closure must fail.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C15",
      "name": "Uncertainty covariance, sensitivity, and identifiability",
      "question": "Are uncertainties, correlations, parameter sensitivities, degeneracies, and truncation errors propagated through the full map?",
      "formal": "For output $y=f(x)$ require\n\\[\n\\Sigma_y=J_f\\Sigma_xJ_f^T+\\Sigma_{\\rm trunc}+\\Sigma_{\\rm scheme}+\\Sigma_{\\rm model},\n\\]\nand publish rank/condition diagnostics for the inverse or identification map.",
      "inputs": [
        "input covariance",
        "Jacobian/sensitivity map",
        "truncation and scheme errors",
        "measurement model"
      ],
      "algorithm": [
        "assemble full covariance including correlations",
        "differentiate/linearize or sample the map",
        "propagate model and truncation uncertainty",
        "compute rank, condition number, and degeneracy directions",
        "perform robustness/worst-case test"
      ],
      "outputs": [
        "uncertainty_covariance_packet",
        "anchor_identifiability_packet"
      ],
      "witness": "Full covariance and sensitivity packet with degeneracies and confidence margins explicit.",
      "fail": "Only central values or independent errors are compared, or a poorly identifiable output is declared uniquely derived.",
      "control": "Use anticorrelated inputs but propagate them as independent; the audit must detect the wrong uncertainty.",
      "old": false,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C16",
      "name": "Hierarchy, naturalness, and radiative-sensitivity diagnosis",
      "question": "Are large scale separations classified by actual protection, sensitivity, and matching structure rather than aesthetic labels?",
      "formal": "For low scale $m_L$ and high scales/parameters $x_a$, publish\n\\[\n\\Delta_a=\\left|\\frac{\\partial\\ln m_L^2}{\\partial\\ln x_a}\\right|\n\\]\nor a more appropriate invariant sensitivity, together with symmetry, topology, sequestering, fixed-point, or dynamical protection claims.",
      "inputs": [
        "matching relations",
        "loop corrections",
        "symmetry/protection certificates",
        "parameter covariance"
      ],
      "algorithm": [
        "identify all high-scale contributions to low-scale quantities",
        "compute regulator/scheme-aware sensitivities",
        "separate coordinate reparameterization from physical tuning",
        "test proposed protection under thresholds and loops",
        "classify diagnosis without using economy as a hard gate"
      ],
      "outputs": [
        "hierarchy_sensitivity_packet",
        "scheme_rg_matching_packet"
      ],
      "witness": "Sensitivity and protection ledger with radiative/threshold robustness and declared claim ceiling.",
      "fail": "A small low-energy scale is called derived or natural solely because a parameter was chosen small or a cancellation occurs at one order.",
      "control": "Tune two high-scale terms to produce a small Higgs mass without protection; the hierarchy remains input-sensitive.",
      "old": false,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C17",
      "name": "Multi-scale EFT, tower matching, truncation, and tail control",
      "question": "Does every finite-mode or finite-operator calculation state its scale interval and control omitted towers/tails?",
      "formal": "For nested effective descriptions $\\mathcal E_0\\subset\\cdots\\subset\\mathcal E_N$, require matching maps, overlap checks, and a tail certificate $\\|R_N\\|\\le\\epsilon_N$ or an explicit finite-scope ceiling.",
      "inputs": [
        "tower spectrum",
        "operator basis",
        "matching scales",
        "RG data",
        "Granularity refinement lattice"
      ],
      "algorithm": [
        "partition scale intervals",
        "match adjacent EFTs",
        "test overlap and decoupling",
        "compute omitted-mode/operator tail or bound",
        "vary truncation/refinement and record convergence",
        "forbid global promotion without a theorem"
      ],
      "outputs": [
        "tower_matching_tail_packet",
        "resolution_refinement_packet"
      ],
      "witness": "Nested matching ledger and convergence/tail certificate with explicit validity interval.",
      "fail": "A zero-mode, finite tower, or finite heat-kernel prefix is promoted to an all-scale claim.",
      "control": "Construct two identical finite prefixes with convergent and divergent tails; global inference must remain OPEN.",
      "old": false,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C18",
      "name": "Time, temperature, horizon, correlation, and state-dependent scales",
      "question": "Are scales that depend on state, history, region, horizon, temperature, or synchronization treated as derived fields/records rather than fixed universal constants?",
      "formal": "For derived scale $s[\\Psi,g,\\rho,t,U]$, publish its defining functional, covariance, support, synchronization convention, variation, and domain of validity.",
      "inputs": [
        "Dynamics histories",
        "Boundary derived supports",
        "Time Synchronization packet",
        "Observer regional records"
      ],
      "algorithm": [
        "enumerate state-/region-dependent scale definitions",
        "derive them from frozen states and supports",
        "transport clocks/temperatures/redshifts consistently",
        "compute variation and uncertainty",
        "test across transitions and horizon/interface changes"
      ],
      "outputs": [
        "state_dependent_scale_packet",
        "same_ruler_packet"
      ],
      "witness": "Definition and transport packet for every nonconstant scale, including support, time standard, and uncertainty.",
      "fail": "A local temperature, horizon radius, correlation length, clock rate, or transition scale is treated as one global fixed ruler.",
      "control": "Use a single coordinate time or temperature across redshifted regions; the same-ruler test must fail.",
      "old": false,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C19",
      "name": "Composite, emergent, and effective scale provenance",
      "question": "Are bound-state masses, condensate scales, correlation lengths, soliton sizes, and emergent effective cutoffs derived from constituent dynamics rather than silently promoted to primitive inputs?",
      "formal": "For emergent scale $M_E$, require a derivation/definition map\n\\[\nM_E=F(\\text{Actors},\\text{interactions},\\text{state},\\mu,\\text{scheme})\n\\]\nwith double-counting and matching checks when an effective Actor is promoted.",
      "inputs": [
        "Actor promotion packet",
        "interaction hypergraph",
        "state/condensate data",
        "matching scheme"
      ],
      "algorithm": [
        "enumerate effective/composite scales",
        "identify constituent and interaction ownership",
        "derive or calibrate the scale explicitly",
        "check matching and double counting",
        "state the EFT validity interval"
      ],
      "outputs": [
        "emergent_scale_packet",
        "parameter_accounting_packet"
      ],
      "witness": "Constituent-to-effective scale derivation and no-double-counting certificate.",
      "fail": "A composite/effective mass or cutoff is treated as a new primitive anchor without provenance or while its constituents remain independently counted.",
      "control": "Introduce a bound-state mass as an independent parameter after deriving it from constituents; the ledger must flag double ownership.",
      "old": false,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C20",
      "name": "Resolution and refinement lattice consistency with Granularity",
      "question": "Do scale cutoffs, observational resolution, discretization, and Granularity classes form a monotone refinement system?",
      "formal": "For refinement order $r_1\\preceq r_2$, require compatible maps\n\\[\n\\mathcal Q_{r_2}\\to\\mathcal Q_{r_1}\n\\]\nand monotone/controlled behavior of records, equivalence classes, spectra, and uncertainties.",
      "inputs": [
        "Granularity cell signatures",
        "cutoff/refinement ladder",
        "Observer resolutions",
        "Dynamics truncations"
      ],
      "algorithm": [
        "freeze the refinement poset",
        "compute coarse-graining/projection maps",
        "test class consistency and noncommuting limits",
        "track discretization and cutoff errors",
        "require convergence or scope ceiling"
      ],
      "outputs": [
        "resolution_refinement_packet",
        "tower_matching_tail_packet"
      ],
      "witness": "Commuting refinement diagram and error/convergence ledger shared with Granularity and Dynamics.",
      "fail": "Changing cutoff/resolution changes the claimed physical class without being detected, or noncommuting limits are silently exchanged.",
      "control": "Take continuum and infinite-volume limits in opposite orders when they disagree; global closure must fail.",
      "old": false,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C21",
      "name": "Candidate-neutral scale grammar, saturation, and exhaustion",
      "question": "Has every scale-bearing object, anchor choice, matching scale, cutoff, threshold, normalization, and admissible scale route been generated and given a disposition?",
      "formal": "Define a frozen grammar $\\mathcal G_{\\rm scl}$ and require\n\\[\nN_{\\rm ungenerated}=N_{\\rm unclassified}=N_{\\rm unresolved\\ aliases}=N_{\\rm omitted\\ scale\\ routes}=0\n\\]\nwithin the declared scope.",
      "inputs": [
        "Shape/Actor grammar",
        "Dynamics operators and histories",
        "Boundary supports",
        "Observer/Granularity test families"
      ],
      "algorithm": [
        "generate all scale objects by typed grammar",
        "canonicalize aliases and convention duplicates",
        "assign provenance and owner",
        "test omitted anchors, thresholds, cutoffs, schemes and scale routes",
        "publish saturation residual"
      ],
      "outputs": [
        "scale_grammar_exhaustion_packet",
        "residual_vector_packet"
      ],
      "witness": "Machine-generated complete scale roster with zero unclassified rows and omitted-route controls.",
      "fail": "One convenient scale assignment or one successful matching route is treated as exhaustive without grammar or theorem.",
      "control": "Add an admissible boundary scale or matching route omitted from the roster; the exhaustion residual must become nonzero.",
      "old": false,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C22",
      "name": "Economy and representative-selection firewall",
      "question": "Is economy used only after physical equivalence and without an undeclared exchange rate among dimensions, parameters, computations, and assumptions?",
      "formal": "For physically equivalent candidates publish a vector\n\\[\n\\mathbf w=(D,N_m,N_c,N_p,N_d,N_b,L_{\\rm desc},C_{\\rm comp})\n\\]\nand use a scalar order only if frozen independently of outcomes.",
      "inputs": [
        "physical equivalence certificate",
        "parameter ledgers",
        "description/computation metrics",
        "ordering rule"
      ],
      "algorithm": [
        "require hard-physics pass first",
        "publish economy vector",
        "freeze any lexicographic/partial order",
        "test invariance under representation changes",
        "forbid economy from rescuing a failed constraint"
      ],
      "outputs": [
        "economy_vector_packet",
        "gate_scale_summary"
      ],
      "witness": "Economy vector and predeclared ordering applied only among one physical equivalence class.",
      "fail": "Simplicity, fewer dimensions, or cheaper computation is used to select a physically failing or distinguishable candidate.",
      "control": "Give the physically wrong candidate a shorter description; it must still lose.",
      "old": true,
      "primary_owner": "Scale",
      "coowners": "Shape|Granularity|Dynamics|Boundary|Observer|Rigidity|Vacuum|Time Synchronization as typed"
    },
    {
      "id": "SCL-C23",
      "name": "Scale-transformation covariance, homogeneity, and anomalous dimensions",
      "old": false,
      "question": "Does every scale-bearing field, operator, observable, spectrum, and response come with its transformation law under a change of physical scale, rather than only a value at one reference point?",
      "formal": "For each typed object $O_i$ and admissible scale transport $s\\mapsto \\lambda s$ or $\\mu\\mapsto e^t\\mu$, require a controlled representation\n\\[\nO_i(\\lambda s)=\\lambda^{\\Delta_i^{\\rm can}}\\sum_j U_{ij}(\\lambda)O_j(s),\n\\qquad\n\\gamma_{ij}=\\frac{d}{d\\ln\\lambda}U_{ij}\\bigg|_{\\lambda=1},\n\\]\nwith canonical dimensions, anomalous-dimension/mixing data, normalization transport, reference/pivot scale, validity interval, and residuals explicit.",
      "inputs": [
        "typed operator/observable roster",
        "canonical dimensions",
        "RG or physical scaling map",
        "normalization and mixing matrices",
        "reference/pivot scales"
      ],
      "algorithm": [
        "generate every admissible physical scale transformation",
        "derive canonical homogeneity degrees",
        "compute or import anomalous dimensions and operator mixing",
        "transport normalizations and covariance",
        "test slopes/exponents over the claimed interval rather than one calibration point",
        "publish residuals and scope ceiling"
      ],
      "outputs": [
        "scale_transformation_packet"
      ],
      "witness": "A complete transformation-law ledger with canonical/anomalous dimensions, mixing, pivot/reference scales, interval tests, and zero unclassified scale responses.",
      "fail": "Two candidates agree at one scale but differ in scaling law, anomalous dimension, or homogeneity and are nevertheless treated as physically equivalent.",
      "control": "Construct two models with the same observable at one pivot scale but different anomalous dimensions; the audit must distinguish them.",
      "primary_owner": "Scale",
      "coowners": "Dynamics|Observer|Shape|Granularity as typed"
    },
    {
      "id": "SCL-C24",
      "name": "Scale-symmetry breaking, trace/Weyl anomaly, and dimensional transmutation",
      "old": false,
      "question": "Are explicit, spontaneous, and anomalous breaking of scale symmetry separated, and are dynamically generated invariant scales derived rather than silently inserted as primitive anchors?",
      "formal": "Require a scale Ward identity of the form\n\\[\n\\left(\\mu\\partial_\\mu+\\beta^a\\partial_{g^a}-\\gamma_i\\mathcal N_i\\right)\\Gamma\n=\\mathcal A_{\\rm scale}+\\mathcal B_{\\rm explicit},\n\\]\nand, when dimensional transmutation is claimed, an RG-invariant generated scale such as\n\\[\n\\Lambda=\\mu\\exp\\!\\left[-\\int^{g(\\mu)}\\frac{dg}{\\beta(g)}\\right]\n\\]\nwith scheme, threshold, measure/Jacobian, boundary, and vacuum provenance controlled.",
      "inputs": [
        "effective action and measure",
        "beta and anomalous-dimension data",
        "explicit breaking terms",
        "Boundary/Vacuum anomaly ledgers",
        "candidate generated scales"
      ],
      "algorithm": [
        "derive the scale/dilatation Ward identity",
        "separate explicit, spontaneous, and anomalous breaking",
        "compute trace/Weyl anomaly and measure contributions",
        "derive every RG-invariant generated scale",
        "test scheme/path/threshold invariance within scope",
        "route vacuum and boundary contributions to their owners"
      ],
      "outputs": [
        "scale_anomaly_transmutation_packet",
        "emergent_scale_packet",
        "scheme_rg_matching_packet"
      ],
      "witness": "A Ward-identity and generated-scale certificate proving the provenance and scoped invariance of every transmuted scale and every trace/Weyl anomaly term.",
      "fail": "A confinement, Planck, vacuum, or other generated scale is called derived without a scale Ward identity/transmutation map, or a trace anomaly is omitted from the scale ledger.",
      "control": "Give two theories the same coupling at one renormalization scale but different beta functions; their generated invariant scales must not be identified.",
      "primary_owner": "Scale",
      "coowners": "Dynamics|Vacuum|Boundary|Observer as typed"
    },
    {
      "id": "SCL-C25",
      "name": "Criticality, universality, finite-size scaling, and crossover",
      "old": false,
      "question": "Are claims near fixed points, phase transitions, continuum limits, or thermodynamic limits supported by critical exponents, universality data, finite-size scaling, and crossover control?",
      "formal": "For control parameter $t$, size $L$, and correlation length $\\xi$, require the applicable scaling form, for example\n\\[\n\\xi\\sim |t|^{-\\nu},\\qquad\n\\Delta(L,t)=L^{-z}F\\!\\left(L^{1/\\nu}t,\\{u_iL^{-\\omega_i}\\}\\right),\n\\]\nwith the fixed point, relevant/irrelevant directions, critical and dynamical exponents, boundary conditions, regulator family, and crossover domain specified.",
      "inputs": [
        "RG fixed-point/flow data",
        "order/control parameters",
        "finite-volume and boundary spectra",
        "thermal/history data",
        "Granularity refinement lattice"
      ],
      "algorithm": [
        "identify candidate fixed points and universality classes",
        "linearize the flow and compute relevant/irrelevant directions",
        "derive critical and dynamical exponents",
        "perform finite-size/refinement scaling tests",
        "compute crossover functions and validity regions",
        "test regulator, boundary, and microscopic-detail independence"
      ],
      "outputs": [
        "critical_scaling_universality_packet",
        "resolution_refinement_packet",
        "state_dependent_scale_packet"
      ],
      "witness": "A universality certificate with fixed point, exponents, finite-size scaling, crossover, regulator/boundary tests, and explicit unresolved directions.",
      "fail": "A finite-volume gap, one correlation length, one truncation fixed point, or one phase-transition point is promoted to a continuum universality claim.",
      "control": "Construct two models with the same correlation length at one point but different $\nu$ or $z$; the audit must keep them distinct.",
      "primary_owner": "Scale",
      "coowners": "Dynamics|Boundary|Granularity|Rigidity|Vacuum as typed"
    },
    {
      "id": "SCL-C26",
      "name": "Extensive, intensive, area/volume/fractal scaling, and regional composition",
      "old": false,
      "question": "Do regional, thermodynamic, entropic, geometric, and information quantities obey the correct scaling and composition law across changes of region size and shape?",
      "formal": "For a scaled region $\\lambda U$, require a typed decomposition such as\n\\[\nQ(\\lambda U)=\\lambda^{d_{\\rm bulk}}Q_{\\rm bulk}(U)+\\lambda^{d_{\\partial}}Q_{\\partial}(\\partial U)+Q_{\\rm corner}+Q_{\\rm top}+Q_{\\rm nonlocal},\n\\]\nwith extensive/intensive/subextensive class, area/volume/fractal or spectral exponent, finite-size corrections, and disjoint-region composition/mutual terms explicit.",
      "inputs": [
        "regional supports and incidence data",
        "Boundary edge/corner packets",
        "Observer regional records",
        "entropy/information/thermodynamic quantities",
        "state-dependent scales"
      ],
      "algorithm": [
        "classify each quantity as extensive, intensive, subextensive, topological, or nonlocal",
        "separate bulk, boundary, corner, defect, and mutual contributions",
        "derive area/volume/fractal/spectral exponents",
        "test disjoint-region composition and finite-size corrections",
        "transport uncertainty and state dependence",
        "state the scaling domain and residuals"
      ],
      "outputs": [
        "composition_scaling_packet",
        "state_dependent_scale_packet",
        "resolution_refinement_packet"
      ],
      "witness": "A regional composition certificate showing the correct scaling exponent and decomposition over multiple region sizes/shapes, with boundary and nonlocal corrections included.",
      "fail": "Two models agree for one region but have different area/volume/extensive scaling and are treated as equivalent, or boundary/mutual terms are hidden in a bulk coefficient.",
      "control": "Match two entropy models at one horizon area, one scaling as area and the other as volume; the audit must reject equivalence.",
      "primary_owner": "Scale",
      "coowners": "Boundary|Observer|Dynamics|Granularity as typed"
    }
  ]
}

SCALE_GATE_CROSSWALK_V4_1.csv27,057 bytes

scale/02_REGISTRIES/SCALE_GATE_CROSSWALK_V4_1.csv

gate_id,source_terminal,scale_role,scale_rows,active_packets,claim_ceiling
Black-hole-singularity,DISSOLVED-GIVEN-root / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C06|SCL-C09|SCL-C10|SCL-C12|SCL-C15|SCL-C17|SCL-C18|SCL-C20|SCL-C21|SCL-C23|SCL-C26,anchor_identifiability_packet|composition_scaling_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|vacuum_stability_value_packet|vacuum_term_ledger|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Born-rule,CLOSED / CERTIFIED-IRREDUCIBLE / RESOLVED +0,CONDITIONAL/SCOPED,SCL-C03|SCL-C13|SCL-C15|SCL-C18|SCL-C20|SCL-C21|SCL-C22,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|economy_vector_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Gap-01,DERIVED-GIVEN-anchor / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C06|SCL-C12|SCL-C14|SCL-C15|SCL-C17|SCL-C20|SCL-C21|SCL-C23|SCL-C24,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|topological_coefficient_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Gap-02,CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C12|SCL-C15|SCL-C17|SCL-C20|SCL-C21|SCL-C24|SCL-C25,anchor_identifiability_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scheme_rg_matching_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Gap-05-stability,CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C09|SCL-C10|SCL-C11|SCL-C12|SCL-C15|SCL-C16|SCL-C18|SCL-C20|SCL-C21|SCL-C23|SCL-C24,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|vacuum_stability_value_packet|vacuum_term_ledger|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Gap-05-value,MEASURED-ANCHOR / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C09|SCL-C10|SCL-C13|SCL-C15|SCL-C21|SCL-C24,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scheme_rg_matching_packet|uncertainty_covariance_packet|vacuum_stability_value_packet|vacuum_term_ledger|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Gap-08,DISSOLVED-GIVEN-root / RESOLVED +0,SCOPED,SCL-C03|SCL-C04|SCL-C13|SCL-C15|SCL-C18|SCL-C20|SCL-C21|SCL-C23|SCL-C25,anchor_identifiability_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Gap-10/BG-10,CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C11|SCL-C12|SCL-C15|SCL-C16|SCL-C18|SCL-C20|SCL-C21|SCL-C23|SCL-C25,anchor_identifiability_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Gap-11,CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C11|SCL-C12|SCL-C15|SCL-C17|SCL-C18|SCL-C19|SCL-C20|SCL-C21|SCL-C23,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|parameter_accounting_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Gap-13,CLOSED / PROJECT-DEPENDENCY / CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C12|SCL-C15|SCL-C17|SCL-C18|SCL-C19|SCL-C20|SCL-C21|SCL-C23|SCL-C26,anchor_identifiability_packet|composition_scaling_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|parameter_accounting_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
Lambda-catastrophe,DISSOLVED-GIVEN-root / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C09|SCL-C10|SCL-C11|SCL-C12|SCL-C13|SCL-C15|SCL-C16|SCL-C20|SCL-C21|SCL-C23|SCL-C24|SCL-C26,anchor_identifiability_packet|composition_scaling_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|vacuum_stability_value_packet|vacuum_term_ledger|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-1,CLOSED / DERIVED-GIVEN-SHAPE / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C04|SCL-C05|SCL-C08|SCL-C15|SCL-C20|SCL-C21|SCL-C22|SCL-C23,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|economy_vector_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|parameter_accounting_packet|provenance_ledger|radius_radion_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-10,DERIVED-GIVEN-anchor / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C11|SCL-C12|SCL-C15|SCL-C16|SCL-C17|SCL-C20|SCL-C21|SCL-C23,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-2,CLOSED / CERTIFIED-IRREDUCIBLE-CATEGORY-FLOOR / RESOLVED +0,SUPPORTING,SCL-C01|SCL-C02|SCL-C03|SCL-C04|SCL-C06|SCL-C13|SCL-C15|SCL-C21,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-3,DERIVED-GIVEN-E / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C04|SCL-C06|SCL-C14|SCL-C15|SCL-C17|SCL-C20|SCL-C21,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|topological_coefficient_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-4,CLOSED / DERIVED-GIVEN-E / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C12|SCL-C14|SCL-C15|SCL-C21,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scheme_rg_matching_packet|topological_coefficient_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-5,DERIVED-GIVEN-anchor / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C05|SCL-C06|SCL-C07|SCL-C08|SCL-C11|SCL-C12|SCL-C13|SCL-C15|SCL-C16|SCL-C17|SCL-C21|SCL-C23|SCL-C24,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|economy_vector_packet|emergent_scale_packet|gap_decoupling_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|multiplier_stiffness_packet|parameter_accounting_packet|provenance_ledger|radius_radion_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-6,DERIVED-GIVEN-anchor / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C05|SCL-C06|SCL-C07|SCL-C08|SCL-C11|SCL-C12|SCL-C15|SCL-C16|SCL-C17|SCL-C20|SCL-C21|SCL-C23|SCL-C25,anchor_identifiability_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|economy_vector_packet|gap_decoupling_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|multiplier_stiffness_packet|parameter_accounting_packet|provenance_ledger|radius_radion_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-7,DISSOLVED-GIVEN-root / RESOLVED +0,LOAD-BEARING,SCL-C03|SCL-C06|SCL-C11|SCL-C12|SCL-C13|SCL-C15|SCL-C16|SCL-C17|SCL-C20|SCL-C21|SCL-C23,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|gap_decoupling_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-8,CLOSED / RESCUED / DISSOLVED-WRONG-RULER + DERIVED-GIVEN-13D-ACTOR / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C08|SCL-C11|SCL-C12|SCL-C13|SCL-C15|SCL-C16|SCL-C17|SCL-C19|SCL-C20|SCL-C21|SCL-C23,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|economy_vector_packet|emergent_scale_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|parameter_accounting_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
SG-9,DERIVED-GIVEN-anchor / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C11|SCL-C12|SCL-C15|SCL-C16|SCL-C17|SCL-C20|SCL-C21|SCL-C23|SCL-C24,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gap_decoupling_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|threshold_phase_history_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
UQF-10,RESOLVED +0 / DERIVED-GIVEN-anchor + CLOSED-NEGATIVE leg,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C05|SCL-C06|SCL-C07|SCL-C08|SCL-C12|SCL-C15|SCL-C17|SCL-C20|SCL-C21|SCL-C23|SCL-C25,anchor_identifiability_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|economy_vector_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|multiplier_stiffness_packet|parameter_accounting_packet|provenance_ledger|radius_radion_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
UQF-14,CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C12|SCL-C15|SCL-C17|SCL-C18|SCL-C20|SCL-C21|SCL-C23|SCL-C25|SCL-C26,anchor_identifiability_packet|composition_scaling_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
UQF-3,CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C12|SCL-C15|SCL-C17|SCL-C18|SCL-C20|SCL-C21|SCL-C25|SCL-C26,anchor_identifiability_packet|composition_scaling_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scheme_rg_matching_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
UQF-4,CLOSED / DERIVED-GIVEN-13D-SHAPE / GLOBAL-ANOMALY-CONSISTENT / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C12|SCL-C14|SCL-C15|SCL-C17|SCL-C20|SCL-C21,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scheme_rg_matching_packet|topological_coefficient_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
UQF-5A/5B,CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C12|SCL-C15|SCL-C16|SCL-C17|SCL-C18|SCL-C20|SCL-C21|SCL-C23|SCL-C24,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gap_decoupling_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
UQF-5C,CLOSED / CERTIFIED-IRREDUCIBLE-FLOOR / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C12|SCL-C15|SCL-C16|SCL-C17|SCL-C20|SCL-C21|SCL-C23|SCL-C25,anchor_identifiability_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
UQF-7,DERIVED-GIVEN-anchor / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C04|SCL-C06|SCL-C12|SCL-C14|SCL-C15|SCL-C17|SCL-C20|SCL-C21,anchor_identifiability_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scheme_rg_matching_packet|topological_coefficient_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
UQF-9,CERTIFIED-IRREDUCIBLE / RESOLVED +0,LOAD-BEARING,SCL-C02|SCL-C03|SCL-C06|SCL-C12|SCL-C14|SCL-C15|SCL-C17|SCL-C20|SCL-C21|SCL-C23|SCL-C24|SCL-C25,anchor_identifiability_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gap_decoupling_packet|gate_scale_summary|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|topological_coefficient_packet|tower_matching_tail_packet|uncertainty_covariance_packet|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.
theta-bar-QCD,DISSOLVED-GIVEN-root / RESOLVED +0,LOAD-BEARING,SCL-C01|SCL-C02|SCL-C03|SCL-C09|SCL-C10|SCL-C12|SCL-C14|SCL-C15|SCL-C16|SCL-C20|SCL-C21|SCL-C23|SCL-C24|SCL-C25,anchor_identifiability_packet|critical_scaling_universality_packet|dependency_hashes|destructive_controls_packet|dimensional_closure_packet|emergent_scale_packet|gate_scale_summary|hierarchy_sensitivity_packet|integrated_scale_certificate_v4|integrated_scale_certificate_v4_1|measured_anchor_firewall_packet|provenance_ledger|residual_vector_packet|resolution_refinement_packet|same_ruler_packet|scale_anomaly_transmutation_packet|scale_authority_manifest|scale_certificate_v3_compatibility|scale_grammar_exhaustion_packet|scale_transformation_packet|scheme_rg_matching_packet|state_dependent_scale_packet|topological_coefficient_packet|tower_matching_tail_packet|uncertainty_covariance_packet|vacuum_stability_value_packet|vacuum_term_ledger|validator_output,No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.

SCALE_GATE_CROSSWALK_V4_1.json1,00,084 bytes

scale/02_REGISTRIES/SCALE_GATE_CROSSWALK_V4_1.json

{
  "schema": "scale-gate-crosswalk-v4.1",
  "date": "2026-08-02",
  "gates": [
    {
      "gate_id": "Black-hole-singularity",
      "source_terminal": "DISSOLVED-GIVEN-root / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C09",
        "SCL-C10",
        "SCL-C12",
        "SCL-C15",
        "SCL-C17",
        "SCL-C18",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C26"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Horizon, curvature, clock, regional, cutoff, and information scales are derived and state-dependent; continuum dissolution cannot erase finite regional scale obligations.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "composition_scaling_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "vacuum_stability_value_packet",
        "vacuum_term_ledger",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Born-rule",
      "source_terminal": "CLOSED / CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "CONDITIONAL/SCOPED",
      "scale_rows": [
        "SCL-C03",
        "SCL-C13",
        "SCL-C15",
        "SCL-C18",
        "SCL-C20",
        "SCL-C21",
        "SCL-C22"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Measurement resolution, calibration roles, subsystem scales, and probability-record normalizations must be frozen without circular use of observed frequencies.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "economy_vector_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Gap-01",
      "source_terminal": "DERIVED-GIVEN-anchor / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C12",
        "SCL-C14",
        "SCL-C15",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C24"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Heat-kernel coefficients, cutoffs, dimensions, boundary normalizations, schemes, and finite-prefix scope require one ruler and explicit tail control.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "topological_coefficient_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Gap-02",
      "source_terminal": "CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C12",
        "SCL-C15",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C24",
        "SCL-C25"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "A mass-gap claim requires a physical normalized gap, infinite-volume/continuum order control, refinement stability, and an honest external-wall ceiling.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Gap-05-stability",
      "source_terminal": "CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C09",
        "SCL-C10",
        "SCL-C11",
        "SCL-C12",
        "SCL-C15",
        "SCL-C16",
        "SCL-C18",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C24"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Static vacuum-offset protection, radiative/threshold robustness, phase history, and residual ownership must remain separate.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "vacuum_stability_value_packet",
        "vacuum_term_ledger",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Gap-05-value",
      "source_terminal": "MEASURED-ANCHOR / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C09",
        "SCL-C10",
        "SCL-C13",
        "SCL-C15",
        "SCL-C21",
        "SCL-C24"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "The measured residual requires exactly one owner and may not be counted as a prediction or as evidence of stability.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scheme_rg_matching_packet",
        "uncertainty_covariance_packet",
        "vacuum_stability_value_packet",
        "vacuum_term_ledger",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Gap-08",
      "source_terminal": "DISSOLVED-GIVEN-root / RESOLVED +0",
      "scale_role": "SCOPED",
      "scale_rows": [
        "SCL-C03",
        "SCL-C04",
        "SCL-C13",
        "SCL-C15",
        "SCL-C18",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C25"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Any dissolution of an assumed early scale must retain explicit clock, temperature, horizon, observation, and anchor roles.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Gap-10/BG-10",
      "source_terminal": "CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C11",
        "SCL-C12",
        "SCL-C15",
        "SCL-C16",
        "SCL-C18",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C25"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Baryogenesis needs thermal, reaction-rate, Hubble, washout, transition, and observational scales on one chronological ruler.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Gap-11",
      "source_terminal": "CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C11",
        "SCL-C12",
        "SCL-C15",
        "SCL-C17",
        "SCL-C18",
        "SCL-C19",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Production, freeze-out, abundance, composite-state, and detector scales require full thermal history and matching.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "parameter_accounting_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Gap-13",
      "source_terminal": "CLOSED / PROJECT-DEPENDENCY / CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C12",
        "SCL-C15",
        "SCL-C17",
        "SCL-C18",
        "SCL-C19",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C26"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Entropy, Page time, horizon area, UV cutoff, microstate, and evaporation scales must be consistently derived and regionally transported.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "composition_scaling_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "parameter_accounting_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "Lambda-catastrophe",
      "source_terminal": "DISSOLVED-GIVEN-root / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C09",
        "SCL-C10",
        "SCL-C11",
        "SCL-C12",
        "SCL-C13",
        "SCL-C15",
        "SCL-C16",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C24",
        "SCL-C26"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "The complete constant-term ledger, shift stability, threshold history, scheme transport, and residual ownership are indispensable.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "composition_scaling_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "vacuum_stability_value_packet",
        "vacuum_term_ledger",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-1",
      "source_terminal": "CLOSED / DERIVED-GIVEN-SHAPE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C04",
        "SCL-C05",
        "SCL-C08",
        "SCL-C15",
        "SCL-C20",
        "SCL-C21",
        "SCL-C22",
        "SCL-C23"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Geometry selection requires honest anchor counts, radii/fluctuation separation, candidate-neutral scale grammar, and non-gating economy.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "economy_vector_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "parameter_accounting_packet",
        "provenance_ledger",
        "radius_radion_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-10",
      "source_terminal": "DERIVED-GIVEN-anchor / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C11",
        "SCL-C12",
        "SCL-C15",
        "SCL-C16",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Precision and threshold claims require tower matching, loop/scheme consistency, sensitivity, and omitted-tail control.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-2",
      "source_terminal": "CLOSED / CERTIFIED-IRREDUCIBLE-CATEGORY-FLOOR / RESOLVED +0",
      "scale_role": "SUPPORTING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C04",
        "SCL-C06",
        "SCL-C13",
        "SCL-C15",
        "SCL-C21"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Gauge-algebra counting is mainly exact, but normalization, cutoff scope, and measured-anchor firewalls remain required for physical interpretation.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-3",
      "source_terminal": "DERIVED-GIVEN-E / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C04",
        "SCL-C06",
        "SCL-C14",
        "SCL-C15",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Family multiplicity and mirror exclusion require normalized index conventions, cutoff/tower scope, and quantified first mirror-capable excitation.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "topological_coefficient_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-4",
      "source_terminal": "CLOSED / DERIVED-GIVEN-E / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C12",
        "SCL-C14",
        "SCL-C15",
        "SCL-C21"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Charge and anomaly ledgers require common hypercharge/trace/global-quotient normalization and quantized coefficient provenance.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scheme_rg_matching_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-5",
      "source_terminal": "DERIVED-GIVEN-anchor / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C05",
        "SCL-C06",
        "SCL-C07",
        "SCL-C08",
        "SCL-C11",
        "SCL-C12",
        "SCL-C13",
        "SCL-C15",
        "SCL-C16",
        "SCL-C17",
        "SCL-C21",
        "SCL-C23",
        "SCL-C24"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "EWSB and hierarchy require complete mass/mixing normalization, physical stiffness ownership, threshold history, sensitivity, and tower matching.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "economy_vector_packet",
        "emergent_scale_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "provenance_ledger",
        "radius_radion_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-6",
      "source_terminal": "DERIVED-GIVEN-anchor / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C05",
        "SCL-C06",
        "SCL-C07",
        "SCL-C08",
        "SCL-C11",
        "SCL-C12",
        "SCL-C15",
        "SCL-C16",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C25"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Moduli claims require every geometric scale fluctuation, kinetic term, potential, mass, mixing, threshold and refinement route.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "economy_vector_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "provenance_ledger",
        "radius_radion_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-7",
      "source_terminal": "DISSOLVED-GIVEN-root / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C03",
        "SCL-C06",
        "SCL-C11",
        "SCL-C12",
        "SCL-C13",
        "SCL-C15",
        "SCL-C16",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Threshold diagnostics must distinguish a wrong-ruler or scope issue from a genuine physical mismatch and cannot use fitted inputs twice.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-8",
      "source_terminal": "CLOSED / RESCUED / DISSOLVED-WRONG-RULER + DERIVED-GIVEN-13D-ACTOR / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C08",
        "SCL-C11",
        "SCL-C12",
        "SCL-C13",
        "SCL-C15",
        "SCL-C16",
        "SCL-C17",
        "SCL-C19",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Flavor transport is a flagship same-ruler problem: 13D-to-4D projection, running masses, chamber factors, calibration roles, and uncertainties must be explicit.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "economy_vector_packet",
        "emergent_scale_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "parameter_accounting_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "SG-9",
      "source_terminal": "DERIVED-GIVEN-anchor / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C11",
        "SCL-C12",
        "SCL-C15",
        "SCL-C16",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C24"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Proton safety requires operator-suppression scales, thresholds, running, tower effects, matrix-element normalization, and uncertainty margins.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "threshold_phase_history_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "UQF-10",
      "source_terminal": "RESOLVED +0 / DERIVED-GIVEN-anchor + CLOSED-NEGATIVE leg",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C05",
        "SCL-C06",
        "SCL-C07",
        "SCL-C08",
        "SCL-C12",
        "SCL-C15",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C25"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Compactification consistency requires full radius/radion, gap, multiplier/stiffness, tower, and refinement ledgers.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "economy_vector_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "provenance_ledger",
        "radius_radion_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "UQF-14",
      "source_terminal": "CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C12",
        "SCL-C15",
        "SCL-C17",
        "SCL-C18",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C25",
        "SCL-C26"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Unitarity claims are scale- and continuation-dependent and require physical energy windows, regulator/refinement stability, and causal clock conventions.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "composition_scaling_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "UQF-3",
      "source_terminal": "CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C12",
        "SCL-C15",
        "SCL-C17",
        "SCL-C18",
        "SCL-C20",
        "SCL-C21",
        "SCL-C25",
        "SCL-C26"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Reflection positivity requires Euclidean/physical normalization, regulator and continuum-limit ordering, and state/temperature scale control.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "composition_scaling_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "UQF-4",
      "source_terminal": "CLOSED / DERIVED-GIVEN-13D-SHAPE / GLOBAL-ANOMALY-CONSISTENT / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C12",
        "SCL-C14",
        "SCL-C15",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Relative/global anomaly and inflow claims require globally quantized coefficients, quotient factors, determinant scales, and regulator/tower scope.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scheme_rg_matching_packet",
        "topological_coefficient_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "UQF-5A/5B",
      "source_terminal": "CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C12",
        "SCL-C15",
        "SCL-C16",
        "SCL-C17",
        "SCL-C18",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C24"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Graviton pole/residue and infrared claims require normalized energy windows, analytic-continuation conventions, higher-mode gaps, and truncation stability.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "UQF-5C",
      "source_terminal": "CLOSED / CERTIFIED-IRREDUCIBLE-FLOOR / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C12",
        "SCL-C15",
        "SCL-C16",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C25"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "A UV-completion claim cannot be inferred from a finite coefficient or truncation; nested-scale convergence and regulator independence are mandatory.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "UQF-7",
      "source_terminal": "DERIVED-GIVEN-anchor / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C04",
        "SCL-C06",
        "SCL-C12",
        "SCL-C14",
        "SCL-C15",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Chiral projection requires common index/charge normalization, mirror gap and tower scope, and boundary/global coefficient consistency.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scheme_rg_matching_packet",
        "topological_coefficient_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "UQF-9",
      "source_terminal": "CERTIFIED-IRREDUCIBLE / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C02",
        "SCL-C03",
        "SCL-C06",
        "SCL-C12",
        "SCL-C14",
        "SCL-C15",
        "SCL-C17",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C24",
        "SCL-C25"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Heat-kernel/UV data require dimension, boundary, normalization, matching, finite-prefix and tail discipline.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gap_decoupling_packet",
        "gate_scale_summary",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "topological_coefficient_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    },
    {
      "gate_id": "theta-bar-QCD",
      "source_terminal": "DISSOLVED-GIVEN-root / RESOLVED +0",
      "scale_role": "LOAD-BEARING",
      "scale_rows": [
        "SCL-C01",
        "SCL-C02",
        "SCL-C03",
        "SCL-C09",
        "SCL-C10",
        "SCL-C12",
        "SCL-C14",
        "SCL-C15",
        "SCL-C16",
        "SCL-C20",
        "SCL-C21",
        "SCL-C23",
        "SCL-C24",
        "SCL-C25"
      ],
      "required_packets": [
        "scale_authority_manifest",
        "provenance_ledger",
        "same_ruler_packet",
        "dimensional_closure_packet",
        "anchor_identifiability_packet",
        "radius_radion_ledger",
        "gap_decoupling_packet",
        "multiplier_stiffness_packet",
        "parameter_accounting_packet",
        "vacuum_term_ledger",
        "vacuum_stability_value_packet",
        "threshold_phase_history_packet",
        "scheme_rg_matching_packet",
        "measured_anchor_firewall_packet",
        "topological_coefficient_packet",
        "uncertainty_covariance_packet",
        "hierarchy_sensitivity_packet",
        "tower_matching_tail_packet",
        "state_dependent_scale_packet",
        "emergent_scale_packet",
        "resolution_refinement_packet",
        "scale_grammar_exhaustion_packet",
        "economy_vector_packet",
        "scale_certificate_v3_compatibility",
        "integrated_scale_certificate_v4",
        "residual_vector_packet",
        "destructive_controls_packet",
        "gate_scale_summary",
        "dependency_hashes",
        "validator_output",
        "scale_transformation_packet",
        "scale_anomaly_transmutation_packet",
        "critical_scaling_universality_packet",
        "composition_scaling_packet",
        "integrated_scale_certificate_v4_1"
      ],
      "discipline": "Topological angle, determinant phase, anomaly normalization, radiative stability, and measured residual roles require one global scale/provenance ledger.",
      "external_dependencies": [
        "Shape",
        "Granularity",
        "Dynamics",
        "Boundary",
        "Observer",
        "Rigidity",
        "Vacuum",
        "Time Synchronization as applicable"
      ],
      "claim_ceiling": "No gate terminal may exceed the weakest required Scale row; missing evidence is OPEN and NOT-APPLICABLE requires a type proof.",
      "active_packets": [
        "anchor_identifiability_packet",
        "critical_scaling_universality_packet",
        "dependency_hashes",
        "destructive_controls_packet",
        "dimensional_closure_packet",
        "emergent_scale_packet",
        "gate_scale_summary",
        "hierarchy_sensitivity_packet",
        "integrated_scale_certificate_v4",
        "integrated_scale_certificate_v4_1",
        "measured_anchor_firewall_packet",
        "provenance_ledger",
        "residual_vector_packet",
        "resolution_refinement_packet",
        "same_ruler_packet",
        "scale_anomaly_transmutation_packet",
        "scale_authority_manifest",
        "scale_certificate_v3_compatibility",
        "scale_grammar_exhaustion_packet",
        "scale_transformation_packet",
        "scheme_rg_matching_packet",
        "state_dependent_scale_packet",
        "topological_coefficient_packet",
        "tower_matching_tail_packet",
        "uncertainty_covariance_packet",
        "vacuum_stability_value_packet",
        "vacuum_term_ledger",
        "validator_output"
      ],
      "inactive_packet_rule": "Every non-active packet remains present with status NOT-APPLICABLE and a gate-specific type proof."
    }
  ]
}

SCALE_PACKET_BUNDLE_JSON_SCHEMA_V4_1.json23,126 bytes

scale/02_REGISTRIES/SCALE_PACKET_BUNDLE_JSON_SCHEMA_V4_1.json

{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "https://physics.magflowmeters.com/schemas/scale-packet-bundle-v4.1.json",
  "title": "BB-SCL-4.1 Scale Packet Bundle",
  "type": "object",
  "required": [
    "scale_authority_manifest",
    "provenance_ledger",
    "same_ruler_packet",
    "dimensional_closure_packet",
    "anchor_identifiability_packet",
    "radius_radion_ledger",
    "gap_decoupling_packet",
    "multiplier_stiffness_packet",
    "parameter_accounting_packet",
    "vacuum_term_ledger",
    "vacuum_stability_value_packet",
    "threshold_phase_history_packet",
    "scheme_rg_matching_packet",
    "measured_anchor_firewall_packet",
    "topological_coefficient_packet",
    "uncertainty_covariance_packet",
    "hierarchy_sensitivity_packet",
    "tower_matching_tail_packet",
    "state_dependent_scale_packet",
    "emergent_scale_packet",
    "resolution_refinement_packet",
    "scale_grammar_exhaustion_packet",
    "economy_vector_packet",
    "scale_certificate_v3_compatibility",
    "integrated_scale_certificate_v4",
    "residual_vector_packet",
    "destructive_controls_packet",
    "gate_scale_summary",
    "dependency_hashes",
    "validator_output",
    "scale_transformation_packet",
    "scale_anomaly_transmutation_packet",
    "critical_scaling_universality_packet",
    "composition_scaling_packet",
    "integrated_scale_certificate_v4_1"
  ],
  "properties": {
    "scale_authority_manifest": {
      "type": "object",
      "required": [
        "authority_id",
        "version",
        "authority_hash",
        "companion_hashes",
        "gate_id",
        "freeze_hash"
      ],
      "properties": {
        "authority_id": {},
        "version": {},
        "authority_hash": {},
        "companion_hashes": {},
        "gate_id": {},
        "freeze_hash": {}
      },
      "additionalProperties": true
    },
    "provenance_ledger": {
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    },
    "state_dependent_scale_packet": {
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    "emergent_scale_packet": {
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        "derivations",
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    },
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        "vectors",
        "ordering_rule",
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        "packet_hashes",
        "residual_vector",
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      "properties": {
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    "residual_vector_packet": {
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        "dimension_mismatches",
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        "unidentified_anchors",
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      ],
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        "controls",
        "expected_outcomes",
        "actual_outcomes",
        "failures"
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      "additionalProperties": true
    },
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      "required": [
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        "physical_question",
        "selected_constraints",
        "inputs",
        "outputs",
        "findings",
        "external_dependencies",
        "claim_ceiling",
        "terminal"
      ],
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    "dependency_hashes": {
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        "gate_contract"
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        "warnings",
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        "anomalous_dimension_matrix",
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        "validity_intervals",
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        "residuals"
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    },
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        "explicit_breaking",
        "spontaneous_breaking",
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        "beta_functions",
        "generated_invariant_scales",
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    "critical_scaling_universality_packet": {
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        "linearized_flow",
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        "finite_size_scaling",
        "crossover_functions",
        "boundary_regulator_tests",
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      "additionalProperties": true
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    "composition_scaling_packet": {
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        "boundary_terms",
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        "topological_terms",
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        "extensive_intensive_class",
        "area_volume_fractal_exponents",
        "composition_tests",
        "finite_size_corrections",
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    "integrated_scale_certificate_v4_1": {
      "type": "object",
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        "gate_id",
        "authority_manifest",
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        "packet_hashes",
        "v4_0_compatibility",
        "source_term_coverage",
        "residual_vector",
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        "terminal",
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      "additionalProperties": true
    }
  },
  "additionalProperties": false
}

SCALE_PACKET_FIELD_REGISTRY_V4_1.json10,914 bytes

scale/02_REGISTRIES/SCALE_PACKET_FIELD_REGISTRY_V4_1.json

{
  "schema": "scale-packet-field-registry-v4.1",
  "date": "2026-08-02",
  "packets": [
    {
      "packet_id": "scale_authority_manifest",
      "required_fields": [
        "authority_id",
        "version",
        "authority_hash",
        "companion_hashes",
        "gate_id",
        "freeze_hash"
      ]
    },
    {
      "packet_id": "provenance_ledger",
      "required_fields": [
        "objects",
        "allowed_classes",
        "owner_uniqueness",
        "orphan_count",
        "mutation_check"
      ]
    },
    {
      "packet_id": "same_ruler_packet",
      "required_fields": [
        "ruler_tuple",
        "tuple_hash",
        "transport_steps",
        "observer_hash",
        "consistency_checks"
      ]
    },
    {
      "packet_id": "dimensional_closure_packet",
      "required_fields": [
        "unit_basis",
        "equations",
        "dimension_vectors",
        "frame_maps",
        "normalization_maps",
        "residuals"
      ]
    },
    {
      "packet_id": "anchor_identifiability_packet",
      "required_fields": [
        "structural_relations",
        "dimension_matrix",
        "rank",
        "nullity",
        "anchors",
        "jacobian",
        "degeneracies"
      ]
    },
    {
      "packet_id": "radius_radion_ledger",
      "required_fields": [
        "scale_sectors",
        "background_values",
        "fluctuations",
        "kinetic_forms",
        "constraints",
        "masses",
        "mixings",
        "observer_couplings"
      ]
    },
    {
      "packet_id": "gap_decoupling_packet",
      "required_fields": [
        "observation_window",
        "sector_gaps",
        "mixing",
        "uncertainty_margin",
        "tail_scope",
        "verdict"
      ]
    },
    {
      "packet_id": "multiplier_stiffness_packet",
      "required_fields": [
        "terms",
        "classification",
        "dimensions",
        "measure_effects",
        "stress",
        "limit_tests"
      ]
    },
    {
      "packet_id": "parameter_accounting_packet",
      "required_fields": [
        "candidate_vectors",
        "object_lists",
        "alias_checks",
        "equal_category_check"
      ]
    },
    {
      "packet_id": "vacuum_term_ledger",
      "required_fields": [
        "terms",
        "frame",
        "scale",
        "scheme",
        "support",
        "owners",
        "metric_dependence",
        "threshold_dependence",
        "uncertainty",
        "protection"
      ]
    },
    {
      "packet_id": "vacuum_stability_value_packet",
      "required_fields": [
        "constant_shift_test",
        "local_response",
        "residual_owner",
        "double_owner_check",
        "separate_verdicts"
      ]
    },
    {
      "packet_id": "threshold_phase_history_packet",
      "required_fields": [
        "thresholds",
        "before_after_actions",
        "matching",
        "constant_shifts",
        "latent_heat",
        "time_scales",
        "history_effects"
      ]
    },
    {
      "packet_id": "scheme_rg_matching_packet",
      "required_fields": [
        "coefficient_vector",
        "beta_functions",
        "scheme_maps",
        "matching_maps",
        "operator_mixing",
        "thresholds",
        "observable_invariance"
      ]
    },
    {
      "packet_id": "measured_anchor_firewall_packet",
      "required_fields": [
        "observables",
        "roles",
        "input_stages",
        "candidate_dependence",
        "prediction_set",
        "duplicate_role_count"
      ]
    },
    {
      "packet_id": "topological_coefficient_packet",
      "required_fields": [
        "terms",
        "form_norms",
        "trace_norms",
        "global_groups",
        "charge_lattices",
        "coefficient_lattices",
        "large_gauge_tests",
        "quotient_factors",
        "orientations",
        "parent_provenance"
      ]
    },
    {
      "packet_id": "uncertainty_covariance_packet",
      "required_fields": [
        "input_covariance",
        "jacobian",
        "truncation_error",
        "scheme_error",
        "model_error",
        "output_covariance",
        "condition_numbers",
        "robustness"
      ]
    },
    {
      "packet_id": "hierarchy_sensitivity_packet",
      "required_fields": [
        "low_scales",
        "high_inputs",
        "sensitivity_measure",
        "loop_order",
        "thresholds",
        "protection_mechanisms",
        "scheme_checks",
        "verdict"
      ]
    },
    {
      "packet_id": "tower_matching_tail_packet",
      "required_fields": [
        "scale_intervals",
        "effective_theories",
        "matching_maps",
        "overlap_tests",
        "omitted_tails",
        "tail_bounds",
        "scope_ceiling"
      ]
    },
    {
      "packet_id": "state_dependent_scale_packet",
      "required_fields": [
        "scale_definitions",
        "states",
        "supports",
        "time_standards",
        "temperature_redshift_maps",
        "variations",
        "uncertainty"
      ]
    },
    {
      "packet_id": "emergent_scale_packet",
      "required_fields": [
        "effective_scales",
        "constituents",
        "interactions",
        "derivations",
        "calibrations",
        "double_counting_checks",
        "validity_intervals"
      ]
    },
    {
      "packet_id": "resolution_refinement_packet",
      "required_fields": [
        "refinement_poset",
        "projection_maps",
        "commutation_tests",
        "limit_order_tests",
        "errors",
        "convergence"
      ]
    },
    {
      "packet_id": "scale_grammar_exhaustion_packet",
      "required_fields": [
        "grammar",
        "generated_roster",
        "aliases",
        "dispositions",
        "omitted_route_controls",
        "residual_counts"
      ]
    },
    {
      "packet_id": "economy_vector_packet",
      "required_fields": [
        "equivalence_class",
        "vectors",
        "ordering_rule",
        "representation_invariance",
        "non_gating_check"
      ]
    },
    {
      "packet_id": "scale_certificate_v3_compatibility",
      "required_fields": [
        "candidate_id",
        "same_ruler_tuple",
        "measured_anchors",
        "calibration_inputs",
        "derived_scales",
        "radius_radion_ledger",
        "compactification_gap",
        "observation_window",
        "field_and_bundle_normalizations",
        "renormalization_scale",
        "scheme_and_matching_order",
        "cutoff_and_floor",
        "constraint_multiplier_dimensions",
        "physical_stiffness_parameters",
        "determinant_contributions",
        "cosmological_term_ledger",
        "threshold_and_phase_transition_ledger",
        "residual_lambda_owner",
        "uncertainty_covariance",
        "parameter_ledger",
        "evidence_hashes",
        "verdict"
      ]
    },
    {
      "packet_id": "integrated_scale_certificate_v4",
      "required_fields": [
        "gate_id",
        "authority_manifest",
        "constraint_row_states",
        "packet_hashes",
        "residual_vector",
        "claim_ceiling",
        "terminal",
        "reopen_triggers"
      ]
    },
    {
      "packet_id": "residual_vector_packet",
      "required_fields": [
        "unowned",
        "dimension_mismatches",
        "wrong_rulers",
        "unidentified_anchors",
        "unclassified_fluctuations",
        "unbounded_gaps",
        "hidden_stiffness",
        "omitted_parameters",
        "vacuum_omissions",
        "double_roles",
        "unquantized_coefficients",
        "uncontrolled_uncertainties",
        "unstable_hierarchies",
        "unbounded_tails",
        "state_scale_errors",
        "emergent_double_counts",
        "refinement_failures",
        "unexhausted_scale_routes"
      ]
    },
    {
      "packet_id": "destructive_controls_packet",
      "required_fields": [
        "controls",
        "expected_outcomes",
        "actual_outcomes",
        "failures"
      ]
    },
    {
      "packet_id": "gate_scale_summary",
      "required_fields": [
        "gate_id",
        "physical_question",
        "selected_constraints",
        "inputs",
        "outputs",
        "findings",
        "external_dependencies",
        "claim_ceiling",
        "terminal"
      ]
    },
    {
      "packet_id": "dependency_hashes",
      "required_fields": [
        "shape",
        "granularity",
        "dynamics",
        "boundary",
        "observer",
        "rigidity",
        "vacuum",
        "time_synchronization",
        "gate_contract"
      ]
    },
    {
      "packet_id": "validator_output",
      "required_fields": [
        "validator_version",
        "checks",
        "errors",
        "warnings",
        "status"
      ]
    },
    {
      "packet_id": "scale_transformation_packet",
      "required_fields": [
        "objects",
        "scale_transformations",
        "canonical_dimensions",
        "anomalous_dimension_matrix",
        "operator_mixing",
        "normalization_transport",
        "reference_or_pivot_scales",
        "validity_intervals",
        "homogeneity_tests",
        "residuals"
      ]
    },
    {
      "packet_id": "scale_anomaly_transmutation_packet",
      "required_fields": [
        "ward_identity",
        "explicit_breaking",
        "spontaneous_breaking",
        "measure_jacobian",
        "trace_or_weyl_anomaly",
        "beta_functions",
        "generated_invariant_scales",
        "scheme_path_tests",
        "threshold_and_boundary_terms",
        "vacuum_terms",
        "residuals"
      ]
    },
    {
      "packet_id": "critical_scaling_universality_packet",
      "required_fields": [
        "control_parameters",
        "order_parameters",
        "fixed_points",
        "linearized_flow",
        "critical_exponents",
        "dynamical_exponent",
        "relevant_irrelevant_directions",
        "finite_size_scaling",
        "crossover_functions",
        "boundary_regulator_tests",
        "universality_verdict",
        "residuals"
      ]
    },
    {
      "packet_id": "composition_scaling_packet",
      "required_fields": [
        "regions",
        "scaling_operations",
        "bulk_terms",
        "boundary_terms",
        "corner_defect_terms",
        "topological_terms",
        "nonlocal_mutual_terms",
        "extensive_intensive_class",
        "area_volume_fractal_exponents",
        "composition_tests",
        "finite_size_corrections",
        "residuals"
      ]
    },
    {
      "packet_id": "integrated_scale_certificate_v4_1",
      "required_fields": [
        "gate_id",
        "authority_manifest",
        "constraint_row_states",
        "packet_hashes",
        "v4_0_compatibility",
        "source_term_coverage",
        "residual_vector",
        "claim_ceiling",
        "terminal",
        "reopen_triggers"
      ]
    }
  ]
}

03_EXECUTION

Execution prompts and Shape–Dynamics integration contracts.

AUTHORITY_PRECEDENCE_AND_COMPANIONS.md346 bytes

scale/03_EXECUTION/AUTHORITY_PRECEDENCE_AND_COMPANIONS.md

Authority precedence and companions

BB-SCL-4.0 controls Scale when selected. It preserves BB-SCL-3.3 exactly. Required companion authorities are Shape V8.1, Granularity V4.0, Dynamics V4.2, Boundary V4.1, and current Observer/Rigidity/Vacuum/Time Synchronization authorities. A companion hash mismatch marks affected packets RESTART-REQUIRED.

GATE_EXECUTION_PROMPT.md1,684 bytes

scale/03_EXECUTION/GATE_EXECUTION_PROMPT.md

Scale V4.1 Gate-Execution Prompt

Treat 01CORE/BBSCL41MAXRIGORALLGATE_SCALE.md as the controlling Scale development authority.

For the selected gate:

Freeze authority hashes, gate contract, candidate grammar, ruler tuple, observable roles, uncertainty policy, regulator/truncation, limit order, and comparison window.
Load 02REGISTRIES/SCALEGATECROSSWALKV4_1.json.
Instantiate all 35 packets from the empty bundle.
Generate the complete scale-bearing roster from Shape, Granularity, Dynamics, Boundary, Rigidity, Vacuum, Observer, and Time Synchronization.
Execute every selected SCL row, including SCL-C23–SCL-C26 when selected. Do not use source terminal labels as evidence.
Execute every active packet. Inactive packets remain present with status: NOT-APPLICABLE and a type proof.
Run all 26 destructive controls: wrong-ruler, fixed-radius/massless-radion, hidden stiffness, measured-as-prediction, one-scale cancellation, finite-tail promotion, unquantized inflow, covariance omission, hierarchy tuning, omitted-scale-route, one-pivot/different-anomalous-dimension, same-coupling/different-transmutation, same-correlation-length/different-universality, and area-versus-volume controls.
Preserve missing evidence as OPEN. Never infer zero, absence, stability, universality, scale symmetry, or exhaustion from silence.
Validate against the V4.1 JSON Schema and run 07SCRIPTS/validatescalepackv4_1.py.
Issue Scale-scoped V3/V4 compatibility certificates, integratedscalecertificatev41, residual vector, claim ceiling, and reopen triggers. Overall gate status remains governed by the gate constitution/status engine.

SCALE_CONSTRAINT_AND_THOUGHT_EXPERIMENT_METHOD.md6,162 bytes

scale/03_EXECUTION/SCALE_CONSTRAINT_AND_THOUGHT_EXPERIMENT_METHOD.md

Scale Constraint and Thought-Experiment Method

Objective

Derive the least complete Scale authority capable of distinguishing every physically different scale/provenance situation present in the current gate corpus, without loading desired gate terminals.

Procedure

Preserve BB-SCL-3.3 exactly.
Extract every Scale-owned distinction and anti-promotion rule.
Sweep all 30 gates for pairs of candidates that old rows could not distinguish.
For each pair, add one candidate-neutral atomic constraint only when no existing row catches the difference.
Specify required inputs, algorithm, outputs, minimal discharge, fail trigger, and destructive control.
Require every new row to be used by at least one gate and every gate to have an explicit Scale profile.
Preserve missing evidence as OPEN; never convert a source terminal into evidence.

Derived counterexamples

SCL-TE-01 — SCL-C01

Insert a dimensionless coefficient with no owner; the validator must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-02 — SCL-C02

Compare a 13D coefficient directly to a 4D canonically normalized observable; the audit must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-03 — SCL-C03

Use a one-chamber 4D running mass against an unprojected higher-dimensional norm; the audit must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-04 — SCL-C04

Give all dimensionless ratios but no independent mass/length anchor; absolute masses must remain OPEN.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-05 — SCL-C05

Fix a radius numerically while retaining a flat radion potential; stability must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-06 — SCL-C06

Choose a central gap above the cutoff whose lower confidence bound enters the window; closure must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-07 — SCL-C07

Stabilize a mode with $\kappa\Phi^2/2$ but label $\kappa$ a multiplier; the audit must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-08 — SCL-C08

Move a fitted real parameter into a boundary datum and claim improved economy; the comparison must reject it.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-09 — SCL-C09

Omit the constraint determinant contribution while claiming a complete vacuum cancellation; the audit must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-10 — SCL-C10

Use exact shift protection but insert the residual from observation; stability may pass while prediction must not.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-11 — SCL-C11

Cancel constants before and after a transition but retain nonzero latent heat; history must remain nontrivial.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-12 — SCL-C12

Tune two terms to cancel at one renormalization scale with no protecting equation; no stability credit is allowed.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-13 — SCL-C13

Fit a mass and then count the same mass as a blind prediction; the audit must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-14 — SCL-C14

Choose an unquantized Chern–Simons coefficient that cancels the local residual; global closure must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-15 — SCL-C15

Use anticorrelated inputs but propagate them as independent; the audit must detect the wrong uncertainty.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-16 — SCL-C16

Tune two high-scale terms to produce a small Higgs mass without protection; the hierarchy remains input-sensitive.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-17 — SCL-C17

Construct two identical finite prefixes with convergent and divergent tails; global inference must remain OPEN.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-18 — SCL-C18

Use a single coordinate time or temperature across redshifted regions; the same-ruler test must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-19 — SCL-C19

Introduce a bound-state mass as an independent parameter after deriving it from constituents; the ledger must flag double ownership.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-20 — SCL-C20

Take continuum and infinite-volume limits in opposite orders when they disagree; global closure must fail.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-21 — SCL-C21

Add an admissible boundary scale or matching route omitted from the roster; the exhaustion residual must become nonzero.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

SCL-TE-22 — SCL-C22

Give the physically wrong candidate a shorter description; it must still lose.

Expected: The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.

04_VALIDATION

Validation reports, manifests, checksums, thought experiments, and counterexamples.

ALL_30_GATE_SCALE_AUDIT_V4_1.md6,452 bytes

scale/04_VALIDATION/ALL_30_GATE_SCALE_AUDIT_V4_1.md

Independent All-30-Gate Scale Sufficiency Audit — V4.1

This second pass compares the Scale authority to the actual gate source rather than checking only registry cardinality. It found four reusable Scale capabilities absent from V4.0 and added them as SCL-C23–SCL-C26. Coverage means the reusable Scale algorithm, witness, fail trigger, control, and packet exist; it does not inherit any gate terminal.

| Gate | Role | Selected rows | V4.1 capability verdict | |---|---|---|---| | Black-hole-singularity | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C06, SCL-C09, SCL-C10, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C26 | COVERED-BY-BB-SCL-4.1 | | Born-rule | CONDITIONAL/SCOPED | SCL-C03, SCL-C13, SCL-C15, SCL-C18, SCL-C20, SCL-C21, SCL-C22 | COVERED-BY-BB-SCL-4.1 | | Gap-01 | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C24 | COVERED-BY-BB-SCL-4.1 | | Gap-02 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C17, SCL-C20, SCL-C21, SCL-C24, SCL-C25 | COVERED-BY-BB-SCL-4.1 | | Gap-05-stability | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C09, SCL-C10, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C24 | COVERED-BY-BB-SCL-4.1 | | Gap-05-value | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C09, SCL-C10, SCL-C13, SCL-C15, SCL-C21, SCL-C24 | COVERED-BY-BB-SCL-4.1 | | Gap-08 | SCOPED | SCL-C03, SCL-C04, SCL-C13, SCL-C15, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C25 | COVERED-BY-BB-SCL-4.1 | | Gap-10/BG-10 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C25 | COVERED-BY-BB-SCL-4.1 | | Gap-11 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C19, SCL-C20, SCL-C21, SCL-C23 | COVERED-BY-BB-SCL-4.1 | | Gap-13 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C19, SCL-C20, SCL-C21, SCL-C23, SCL-C26 | COVERED-BY-BB-SCL-4.1 | | Lambda-catastrophe | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C09, SCL-C10, SCL-C11, SCL-C12, SCL-C13, SCL-C15, SCL-C16, SCL-C20, SCL-C21, SCL-C23, SCL-C24, SCL-C26 | COVERED-BY-BB-SCL-4.1 | | SG-1 | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C04, SCL-C05, SCL-C08, SCL-C15, SCL-C20, SCL-C21, SCL-C22, SCL-C23 | COVERED-BY-BB-SCL-4.1 | | SG-10 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23 | COVERED-BY-BB-SCL-4.1 | | SG-2 | SUPPORTING | SCL-C01, SCL-C02, SCL-C03, SCL-C04, SCL-C06, SCL-C13, SCL-C15, SCL-C21 | COVERED-BY-BB-SCL-4.1 | | SG-3 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C04, SCL-C06, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21 | COVERED-BY-BB-SCL-4.1 | | SG-4 | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C12, SCL-C14, SCL-C15, SCL-C21 | COVERED-BY-BB-SCL-4.1 | | SG-5 | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C05, SCL-C06, SCL-C07, SCL-C08, SCL-C11, SCL-C12, SCL-C13, SCL-C15, SCL-C16, SCL-C17, SCL-C21, SCL-C23, SCL-C24 | COVERED-BY-BB-SCL-4.1 | | SG-6 | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C05, SCL-C06, SCL-C07, SCL-C08, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C25 | COVERED-BY-BB-SCL-4.1 | | SG-7 | LOAD-BEARING | SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C13, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23 | COVERED-BY-BB-SCL-4.1 | | SG-8 | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C08, SCL-C11, SCL-C12, SCL-C13, SCL-C15, SCL-C16, SCL-C17, SCL-C19, SCL-C20, SCL-C21, SCL-C23 | COVERED-BY-BB-SCL-4.1 | | SG-9 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C11, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C24 | COVERED-BY-BB-SCL-4.1 | | UQF-10 | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C05, SCL-C06, SCL-C07, SCL-C08, SCL-C12, SCL-C15, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C25 | COVERED-BY-BB-SCL-4.1 | | UQF-14 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C25, SCL-C26 | COVERED-BY-BB-SCL-4.1 | | UQF-3 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C17, SCL-C18, SCL-C20, SCL-C21, SCL-C25, SCL-C26 | COVERED-BY-BB-SCL-4.1 | | UQF-4 | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C12, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21 | COVERED-BY-BB-SCL-4.1 | | UQF-5A/5B | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C18, SCL-C20, SCL-C21, SCL-C23, SCL-C24 | COVERED-BY-BB-SCL-4.1 | | UQF-5C | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C15, SCL-C16, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C25 | COVERED-BY-BB-SCL-4.1 | | UQF-7 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C04, SCL-C06, SCL-C12, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21 | COVERED-BY-BB-SCL-4.1 | | UQF-9 | LOAD-BEARING | SCL-C02, SCL-C03, SCL-C06, SCL-C12, SCL-C14, SCL-C15, SCL-C17, SCL-C20, SCL-C21, SCL-C23, SCL-C24, SCL-C25 | COVERED-BY-BB-SCL-4.1 | | theta-bar-QCD | LOAD-BEARING | SCL-C01, SCL-C02, SCL-C03, SCL-C09, SCL-C10, SCL-C12, SCL-C14, SCL-C15, SCL-C16, SCL-C20, SCL-C21, SCL-C23, SCL-C24, SCL-C25 | COVERED-BY-BB-SCL-4.1 |

New second-pass constraints

SCL-C23: A one-scale value does not determine the scaling law; gates using heat-kernel weights, spectral slopes, high-energy amplitudes, or hierarchy powers require explicit homogeneity/anomalous-dimension transport.
SCL-C24: Trace/Weyl anomalies and dimensional transmutation generate physical scales that are neither primitive anchors nor ordinary matching outputs; they need a separate Ward-identity certificate.
SCL-C25: Finite-volume, finite-cutoff, or one-truncation evidence does not determine a continuum universality class or critical exponents.
SCL-C26: Area-law, volume-law, extensive, subextensive, and nonlocal regional composition can differ even when one characteristic radius or entropy value matches.

Sufficiency verdict

30/30 canonical gates have explicit Scale profiles.
26/26 Scale constraints are used by at least one gate.
Every gate bundle contains all 35 packet types; inactive packets require a type proof.
Every selected row has its required outputs in the gate active-packet set.
Missing candidate-specific calculations remain OPEN and are not building-block omissions.
No additional reusable Scale capability was identified within the current 30-gate corpus after the V4.1 repairs.

CONTROL_RESULTS_V4_1.json70 bytes

scale/04_VALIDATION/CONTROL_RESULTS_V4_1.json

{
  "status": "PASS",
  "passed": 26,
  "failed": 0,
  "errors": []
}

HOSTILE_REVIEW_V4_1.md646 bytes

scale/04_VALIDATION/HOSTILE_REVIEW_V4_1.md

Hostile Scale V4.1 review

Status: PASS

The second independent review checked:

exact BB-SCL-3.3 and BB-SCL-4.0 preservation;
26 unique atomic constraints and 30 canonical gates;
all 35 packet schemas and full-bundle presence;
selected-row output to active-packet integrity;
source-derived coverage of scaling laws, scale anomalies/transmutation, critical universality, and regional composition;
no gate-terminal inheritance;
explicit OPEN/NOT-APPLICABLE discipline.

No additional reusable Scale capability was identified within the current 30-gate corpus after V4.1. This does not certify candidate-specific gate evidence.

MANIFEST.json19,128 bytes

scale/04_VALIDATION/MANIFEST.json

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SECOND_PASS_FINDINGS_V4_1.md726 bytes

scale/04_VALIDATION/SECOND_PASS_FINDINGS_V4_1.md

Scale V4.1 second-pass findings

The first V4.0 pass was preservation- and schema-complete for its 22 constraints, but the all-gate source review exposed five operational/physical gaps:

No explicit scale-transformation/homogeneity/anomalous-dimension row.
No explicit trace/Weyl-anomaly and dimensional-transmutation row.
No explicit critical-universality/finite-size/crossover row.
No explicit area/volume/extensive regional-composition row.
The core required every packet type, while the gate crosswalk listed only selected packet subsets.

V4.1 repairs all five. Every bundle now contains all 35 packet types; the crosswalk separately identifies active packets, and inactive packets require a type proof.

SHA256SUMS.txt12,482 bytes

scale/04_VALIDATION/SHA256SUMS.txt

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SOURCE_TERM_COVERAGE_V4_1.json1,664 bytes

scale/04_VALIDATION/SOURCE_TERM_COVERAGE_V4_1.json

{
  "SCL-C23": {
    "source_concepts": [
      "dimensional homogeneity",
      "anomalous dimension",
      "spectral tilt/pivot scaling",
      "high-energy amplitude scaling"
    ],
    "gates": [
      "Black-hole-singularity",
      "Gap-01",
      "Gap-05-stability",
      "Gap-08",
      "Gap-10/BG-10",
      "Gap-11",
      "Gap-13",
      "Lambda-catastrophe",
      "SG-1",
      "SG-10",
      "SG-5",
      "SG-6",
      "SG-7",
      "SG-8",
      "SG-9",
      "UQF-10",
      "UQF-14",
      "UQF-5A/5B",
      "UQF-5C",
      "UQF-9",
      "theta-bar-QCD"
    ]
  },
  "SCL-C24": {
    "source_concepts": [
      "trace/Weyl anomaly",
      "odd-dimensional absence of scale anomaly",
      "dimensional transmutation",
      "RG-invariant confinement scale"
    ],
    "gates": [
      "Gap-01",
      "Gap-02",
      "Gap-05-stability",
      "Gap-05-value",
      "Lambda-catastrophe",
      "SG-5",
      "SG-9",
      "UQF-5A/5B",
      "UQF-9",
      "theta-bar-QCD"
    ]
  },
  "SCL-C25": {
    "source_concepts": [
      "universality class",
      "finite-volume/continuum limit",
      "critical exponents",
      "crossover/phase scaling"
    ],
    "gates": [
      "Gap-02",
      "Gap-08",
      "Gap-10/BG-10",
      "SG-6",
      "UQF-10",
      "UQF-14",
      "UQF-3",
      "UQF-5C",
      "UQF-9",
      "theta-bar-QCD"
    ]
  },
  "SCL-C26": {
    "source_concepts": [
      "area law",
      "volume law",
      "extensivity/cluster composition",
      "regional entropy scaling"
    ],
    "gates": [
      "Black-hole-singularity",
      "Gap-13",
      "Lambda-catastrophe",
      "UQF-14",
      "UQF-3"
    ]
  }
}

THOUGHT_EXPERIMENTS_AND_CONTROLS.json12,541 bytes

scale/04_VALIDATION/THOUGHT_EXPERIMENTS_AND_CONTROLS.json

{
  "schema": "scale-thought-experiments-v4.1",
  "tests": [
    {
      "test_id": "SCL-TE-01",
      "constraint_id": "SCL-C01",
      "scenario": "Insert a dimensionless coefficient with no owner; the validator must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Universal scale provenance and unique ownership is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-02",
      "constraint_id": "SCL-C02",
      "scenario": "Compare a 13D coefficient directly to a 4D canonically normalized observable; the audit must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Dimensional, unit, frame, and normalization closure is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-03",
      "constraint_id": "SCL-C03",
      "scenario": "Use a one-chamber 4D running mass against an unprojected higher-dimensional norm; the audit must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Same-ruler comparison and Observer transport is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-04",
      "constraint_id": "SCL-C04",
      "scenario": "Give all dimensionless ratios but no independent mass/length anchor; absolute masses must remain OPEN.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Structural information versus absolute scale and anchor identifiability is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-05",
      "constraint_id": "SCL-C05",
      "scenario": "Fix a radius numerically while retaining a flat radion potential; stability must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Background scale versus physical fluctuation is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-06",
      "constraint_id": "SCL-C06",
      "scenario": "Choose a central gap above the cutoff whose lower confidence bound enters the window; closure must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Quantitative gaps, decoupling, and observation windows is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-07",
      "constraint_id": "SCL-C07",
      "scenario": "Stabilize a mode with $\\kappa\\Phi^2/2$ but label $\\kappa$ a multiplier; the audit must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Constraint multiplier versus physical stiffness is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-08",
      "constraint_id": "SCL-C08",
      "scenario": "Move a fitted real parameter into a boundary datum and claim improved economy; the comparison must reject it.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Equal parameter, discrete-choice, boundary, and global accounting is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-09",
      "constraint_id": "SCL-C09",
      "scenario": "Omit the constraint determinant contribution while claiming a complete vacuum cancellation; the audit must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Complete vacuum and cosmological-term ledger is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-10",
      "constraint_id": "SCL-C10",
      "scenario": "Use exact shift protection but insert the residual from observation; stability may pass while prediction must not.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Vacuum stability versus residual-value ownership is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-11",
      "constraint_id": "SCL-C11",
      "scenario": "Cancel constants before and after a transition but retain nonzero latent heat; history must remain nontrivial.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Threshold, phase-transition, and history scale ledger is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-12",
      "constraint_id": "SCL-C12",
      "scenario": "Tune two terms to cancel at one renormalization scale with no protecting equation; no stability credit is allowed.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Renormalization, scheme, RG, and matching transport is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-13",
      "constraint_id": "SCL-C13",
      "scenario": "Fit a mass and then count the same mass as a blind prediction; the audit must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Measured-anchor, calibration, prediction, and residual firewall is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-14",
      "constraint_id": "SCL-C14",
      "scenario": "Choose an unquantized Chern–Simons coefficient that cancels the local residual; global closure must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Topological and inflow coefficient normalization and quantization is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-15",
      "constraint_id": "SCL-C15",
      "scenario": "Use anticorrelated inputs but propagate them as independent; the audit must detect the wrong uncertainty.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Uncertainty covariance, sensitivity, and identifiability is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-16",
      "constraint_id": "SCL-C16",
      "scenario": "Tune two high-scale terms to produce a small Higgs mass without protection; the hierarchy remains input-sensitive.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Hierarchy, naturalness, and radiative-sensitivity diagnosis is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-17",
      "constraint_id": "SCL-C17",
      "scenario": "Construct two identical finite prefixes with convergent and divergent tails; global inference must remain OPEN.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Multi-scale EFT, tower matching, truncation, and tail control is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-18",
      "constraint_id": "SCL-C18",
      "scenario": "Use a single coordinate time or temperature across redshifted regions; the same-ruler test must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Time, temperature, horizon, correlation, and state-dependent scales is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-19",
      "constraint_id": "SCL-C19",
      "scenario": "Introduce a bound-state mass as an independent parameter after deriving it from constituents; the ledger must flag double ownership.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Composite, emergent, and effective scale provenance is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-20",
      "constraint_id": "SCL-C20",
      "scenario": "Take continuum and infinite-volume limits in opposite orders when they disagree; global closure must fail.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Resolution and refinement lattice consistency with Granularity is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-21",
      "constraint_id": "SCL-C21",
      "scenario": "Add an admissible boundary scale or matching route omitted from the roster; the exhaustion residual must become nonzero.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Candidate-neutral scale grammar, saturation, and exhaustion is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-22",
      "constraint_id": "SCL-C22",
      "scenario": "Give the physically wrong candidate a shorter description; it must still lose.",
      "expected": "The candidate is rejected or its claim ceiling is reduced; the named Scale row cannot PASS.",
      "purpose": "Demonstrate that Economy and representative-selection firewall is logically independent and gate-relevant.",
      "status": "PASS"
    },
    {
      "test_id": "SCL-TE-23",
      "constraint_id": "SCL-C23",
      "counterexample": "Construct two models with the same observable at one pivot scale but different anomalous dimensions; the audit must distinguish them.",
      "expected": "FAIL-IF-NOT-DETECTED",
      "status": "PASS",
      "rationale": "The new constraint distinguishes a pair that can satisfy V4.0 characteristic-scale ledgers while differing physically across scale transformations or region/refinement classes."
    },
    {
      "test_id": "SCL-TE-24",
      "constraint_id": "SCL-C24",
      "counterexample": "Give two theories the same coupling at one renormalization scale but different beta functions; their generated invariant scales must not be identified.",
      "expected": "FAIL-IF-NOT-DETECTED",
      "status": "PASS",
      "rationale": "The new constraint distinguishes a pair that can satisfy V4.0 characteristic-scale ledgers while differing physically across scale transformations or region/refinement classes."
    },
    {
      "test_id": "SCL-TE-25",
      "constraint_id": "SCL-C25",
      "counterexample": "Construct two models with the same correlation length at one point but different $\nu$ or $z$; the audit must keep them distinct.",
      "expected": "FAIL-IF-NOT-DETECTED",
      "status": "PASS",
      "rationale": "The new constraint distinguishes a pair that can satisfy V4.0 characteristic-scale ledgers while differing physically across scale transformations or region/refinement classes."
    },
    {
      "test_id": "SCL-TE-26",
      "constraint_id": "SCL-C26",
      "counterexample": "Match two entropy models at one horizon area, one scaling as area and the other as volume; the audit must reject equivalence.",
      "expected": "FAIL-IF-NOT-DETECTED",
      "status": "PASS",
      "rationale": "The new constraint distinguishes a pair that can satisfy V4.0 characteristic-scale ledgers while differing physically across scale transformations or region/refinement classes."
    }
  ]
}

VALIDATION_REPORT_V4_1.json92 bytes

scale/04_VALIDATION/VALIDATION_REPORT_V4_1.json

{
  "status": "PASS",
  "constraints": 26,
  "gates": 30,
  "packets": 35,
  "errors": []
}

VALIDATION_REPORT_V4_1.md146 bytes

scale/04_VALIDATION/VALIDATION_REPORT_V4_1.md

Scale V4.1 validation

Status: PASS
Constraints: 26/26
Gates: 30/30
Packet schemas: 35/35
Destructive controls: 26/26
Errors: 0

05_REGRESSION

Regression and calibration reports for the gate-closure workflow.

CALIBRATION_SYNTHESIS_V4_1.md634 bytes

scale/05_REGRESSION/CALIBRATION_SYNTHESIS_V4_1.md

Scale V4.1 calibration synthesis

The second-pass calibration set targets the four added capabilities:

Gap-01: homogeneity and trace-anomaly classification;
Gap-02: dimensional transmutation and universality/limit discipline;
Gap-08: spectral/pivot scaling;
Gap-13: area/volume regional composition;
UQF-5C: critical exponents and truncation universality;
UQF-9: odd-dimensional scale-anomaly absence;
UQF-14: extensivity and cluster composition.

The block now contains the reusable algorithms and certificates. Candidate-specific calculations and external theorems remain gate evidence, not building-block content.

GAP01_SCALING_REPORT.md254 bytes

scale/05_REGRESSION/GAP01_SCALING_REPORT.md

GAP01 SCALING

Gap-01 now explicitly tests weight homogeneity and the presence/absence of a trace-scale anomaly rather than relying only on dimensional closure.

Result: REUSABLE SCALE CAPABILITY PRESENT IN BB-SCL-4.1; GATE TERMINAL NOT INHERITED.

GAP02_UNIVERSALITY_REPORT.md251 bytes

scale/05_REGRESSION/GAP02_UNIVERSALITY_REPORT.md

GAP02 UNIVERSALITY

Gap-02 now separates the RG-generated confinement scale from a primitive anchor and requires finite-size/continuum universality evidence.

Result: REUSABLE SCALE CAPABILITY PRESENT IN BB-SCL-4.1; GATE TERMINAL NOT INHERITED.

GAP05_REPORT.md347 bytes

scale/05_REGRESSION/GAP05_REPORT.md

Gap-05 — vacuum stability and value

Scale V4.0 produces separate stability and residual-value packets. Exact shift protection may PASS while the observed value remains MEASURED-RESIDUAL or OPEN. Threshold and phase history remain separate from static cancellation.

Result: BUILDING-BLOCK CAPABILITY PRESENT; GATE TERMINAL NOT INHERITED.

GAP08_SPECTRAL_SCALING_REPORT.md230 bytes

scale/05_REGRESSION/GAP08_SPECTRAL_SCALING_REPORT.md

GAP08 SPECTRAL SCALING

Gap-08 now requires pivot/reference-scale transport, spectral scaling exponents, and crossover/validity control.

Result: REUSABLE SCALE CAPABILITY PRESENT IN BB-SCL-4.1; GATE TERMINAL NOT INHERITED.

GAP13_COMPOSITION_REPORT.md241 bytes

scale/05_REGRESSION/GAP13_COMPOSITION_REPORT.md

GAP13 COMPOSITION

Gap-13 now distinguishes area, volume, boundary, corner, topological, and nonlocal entropy scaling across multiple region sizes.

Result: REUSABLE SCALE CAPABILITY PRESENT IN BB-SCL-4.1; GATE TERMINAL NOT INHERITED.

LAMBDA_REPORT.md323 bytes

scale/05_REGRESSION/LAMBDA_REPORT.md

Lambda catastrophe

The complete vacuum ledger, scheme transport, threshold/phase history, uncertainty, and residual ownership are mandatory. Any “dissolution” must show which premise is removed while preserving the finite physical ledger.

Result: BUILDING-BLOCK CAPABILITY PRESENT; GATE TERMINAL NOT INHERITED.

SG10_REPORT.md318 bytes

scale/05_REGRESSION/SG10_REPORT.md

SG-10 — precision/tower thresholds

Scale V4.0 requires nested EFT/tower matching, overlap tests, truncation/refinement stability, and omitted-tail control. A finite threshold calculation cannot be promoted beyond its declared interval.

Result: BUILDING-BLOCK CAPABILITY PRESENT; GATE TERMINAL NOT INHERITED.

SG5_REPORT.md399 bytes

scale/05_REGRESSION/SG5_REPORT.md

SG-5 — EWSB and hierarchy

Scale V4.0 correctly demands mass/mixing normalization, radius/fluctuation separation, stiffness ownership, hierarchy sensitivity, threshold history, and tower matching. Existing source claims are not re-certified here; candidate-specific Dynamics/Rigidity/Vacuum evidence remains required.

Result: BUILDING-BLOCK CAPABILITY PRESENT; GATE TERMINAL NOT INHERITED.

SG7_REPORT.md375 bytes

scale/05_REGRESSION/SG7_REPORT.md

SG-7 — thresholds and diagnostic scope

Scale V4.0 distinguishes a wrong-ruler, calibration, threshold, scheme, or finite-tower issue from a physical mismatch. A diagnostic or dissolved terminal must identify which scale premise fails; it cannot be inferred from one convenient matching scale.

Result: BUILDING-BLOCK CAPABILITY PRESENT; GATE TERMINAL NOT INHERITED.

SG8_REPORT.md392 bytes

scale/05_REGRESSION/SG8_REPORT.md

SG-8 — flavor and wrong-ruler control

The same-ruler and measured-anchor firewalls require the complete 13D-to-4D projection, chamber normalization, running scale, scheme, covariance, and calibration history. This directly catches the historical wrong-ruler failure mode without assuming the rescued terminal.

Result: BUILDING-BLOCK CAPABILITY PRESENT; GATE TERMINAL NOT INHERITED.

UQF14_EXTENSIVITY_REPORT.md227 bytes

scale/05_REGRESSION/UQF14_EXTENSIVITY_REPORT.md

UQF14 EXTENSIVITY

UQF-14 now requires regional/extensive composition and cluster scaling, not merely a characteristic cutoff or gap.

Result: REUSABLE SCALE CAPABILITY PRESENT IN BB-SCL-4.1; GATE TERMINAL NOT INHERITED.

UQF5C_CRITICAL_REPORT.md236 bytes

scale/05_REGRESSION/UQF5C_CRITICAL_REPORT.md

UQF5C CRITICAL

UQF-5C now treats fixed-point coordinates and critical exponents as truncation/universality data, not one-truncation evidence.

Result: REUSABLE SCALE CAPABILITY PRESENT IN BB-SCL-4.1; GATE TERMINAL NOT INHERITED.

UQF9_SCALE_ANOMALY_REPORT.md262 bytes

scale/05_REGRESSION/UQF9_SCALE_ANOMALY_REPORT.md

UQF9 SCALE ANOMALY

UQF-9 now explicitly certifies the odd-dimensional absence of the local trace-scale anomaly and separates it from power divergences and scheme data.

Result: REUSABLE SCALE CAPABILITY PRESENT IN BB-SCL-4.1; GATE TERMINAL NOT INHERITED.

06_SOURCES

Preserved archival source material, including prior Scale packages and related building blocks.

BB_BND_4_1_MAX_RIGOR_FULL_GATE_CLOSURE_BOUNDARY.md1,11,318 bytes

scale/06_SOURCES/BB_BND_4_1_MAX_RIGOR_FULL_GATE_CLOSURE_BOUNDARY.md

--- title: "BB-BND-4.1 — Maximum-Rigor Boundary, Domain, Gluing, and Anomaly-Descent Gate-Closure Authority" buildingblockid: "BB-BND-4.1" version: "4.1" date: "2026-08-02" status: "MAXIMUM-RIGOR DEVELOPMENT AUTHORITY — ALL-GATE DERIVED — OPERATIONALLY COMPLETE — CALIBRATION REQUIRED" supersedesfordevelopment: "BB-BND-4.0 + BB-BND-A-1 + BB-BND-B-1 + BB-AD-1, without deleting their exact source" ---

BB-BND-4.1 — Maximum-Rigor Boundary, Domain, Gluing, and Anomaly-Descent Gate-Closure Authority

0. Status and claim ceiling

This is a development authority for gate execution. It preserves every substantive obligation in BB-BND-A-1, BB-BND-B-1, the inherited BB-BND-1.1 method, and BB-AD-1, and adds only constraints forced by the thirty-gate corpus and destructive thought experiments. It does not ratify any gate, calculate a missing eta/bordism invariant, or convert old evidence into PASS.

BOUNDARY V4.1 MAY DEFINE, GENERATE, TEST, AND CERTIFY BOUNDARY OBLIGATIONS.
IT MAY NOT ASSUME A DESIRED DOMAIN, INFLOW, EDGE SECTOR, OR GLOBAL PHASE.
MISSING EVIDENCE IS OPEN.
LOCAL CANCELLATION IS NOT GLOBAL TRIVIALIZATION.
STATIC DOMAIN VALIDITY IS NOT TIME-DEPENDENT DOMAIN VALIDITY.
GLOBAL CONSERVATION IS NOT REGIONAL/HORIZON FLUX CLOSURE.

1. Owned physical question

Boundary asks: Given the complete parent Shape and Dynamics, what additional supports, domains, variational terms, edge sectors, anomaly data, gluing laws, and flux records are required so that the theory is physically and quantum mechanically defined on every regular, singular, derived, and regional support?

It owns physical boundaries, orbifold fixed sets, defects, interfaces, corners, junctions, cuts, horizons, asymptotic components, operator domains, boundary variational data, local/global anomalies, quantized inflow, determinant lines, edge/factorization sectors, and boundary refinement.

It does not own the bulk Stage, bulk equations, measured Scale anchors, Observer interpretation, or gate governance, but it consumes and returns typed packets to those owners.

2. Complete Boundary object

Define the Boundary object

\[ \mathfrak B= (\mathcal S{\partial},\mathcal I{\partial},\mathcal D{\partial}, S{\partial},\mathcal J{\partial},\mathcal E{\partial}, \mathcal A{\rm loc},\mathcal I{\rm inflow},\mathcal L{\det}, \mathcal F{\rm edge},\mathcal C{\rm causal},\mathcal R{\partial}). \]

The entries are respectively the support/stratum shelf, incidence category, operator-domain functor, variational boundary/corner action, junction/reaction system, edge/regional algebra, local anomaly theory, quantized inflow system, determinant/anomaly line with gluing, factorization data, causal/asymptotic data, and refinement/RG system.

Boundary completeness is not a property of a manifold alone. It is a fixed point of the simultaneous closure of support generation, domain construction, variation, kernel calculation, anomaly descent, inflow, gluing, regional factorization, causal flux, and refinement.

3. Interfaces

| Interface | Boundary consumes | Boundary emits | Firewall | |---|---|---|---| | Shape | Stage strata, SHP-X01 derived supports, Actor/Co-Actor owners, Rulebook parities/global form | typed supports, domains, edge-sector dispositions | Boundary may not add a fundamental Stage factor or Actor merely to close a gate | | Dynamics | operators, currents, histories, constraints, interactions | lawful domains, boundary equations, kernels, flux and anomaly packets | Boundary does not replace bulk dynamics; Dynamics cannot select a domain without Boundary | | Granularity | candidate/test saturation and operational records | complete stratum/domain/edge inventory and exact boundary records | exact anomaly/domain/global data are never tolerance-merged | | Scale | units, cutoff, normalization, coefficient provenance | normalized measures, quantization lattices, boundary gaps and refinement scope | no factor or inflow coefficient may be fitted post-target | | Rigidity | deformation grammar | boundary-position/domain/edge deformation dispositions | a fixed boundary value is not absence of a boundary mode | | Vacuum | background and offset response | boundary stress, vacuum/counterterm side effects | anomaly repair is not vacuum-neutral by default | | Observer | accessible records and regional map | boundary/horizon/edge record packet | inaccessible is not absent without a type proof | | Interdependence | branch hashes and dependency graph | stale propagation and gluing dependencies | no mixed-branch boundary certificate | | Time Synchronization | event classes and loop closure | time-dependent support/domain and causal-boundary packets | equal coordinate time is not a boundary-history theorem | | CSE | freeze, candidate neutrality, status engine | row states and exact terminal | Boundary never manually promotes OPEN to PASS |

4. Constraint-derived construction method

Freeze the parent branch, gate scope, observer, Scale packet, support grammar, global group, tangential structure, and permitted terminal taxonomy.
Reconstruct every legacy Boundary obligation without weakening it.
For each gate, construct two candidates that agree on the current Boundary rows but differ in one physical outcome.
Add a new row only when the difference cannot be assigned to another owner and survives destructive controls.
Apply the row to every gate where its type can occur; require a type proof for N/A.
Run target-masked calibration; failures repair the reusable row and propagate to every mapped gate.

5. Atomic Boundary constraints

BND-C01 — Complete stratified-support inventory

Owners: Boundary + Shape Legacy status: PRESERVED

Requirement. Enumerate every regular stratum, physical boundary, orbifold fixed set, defect, interface, corner, junction, asymptotic component, derived regional support, isotropy group, normal representation, orientation, incidence arrow, localized field, edge variable, allowed gauge transformation, gluing partner, and Observer-accessibility class.

Thought experiment forcing the row. Two candidates can share the same bulk manifold and action while differing by one omitted fixed component carrying a localized kernel or anomaly. Bulk equality therefore does not determine the physical boundary object.

Execution algorithm.

Generate the support shelf from Stage and SHP-X01.
Close the incidence relation under intersections, corners, junctions, orientation reversal, and derived supports.
Assign a stable support ID, support type, dimension, codimension, normal data, global-group restriction, localized content, and owner.
Run an omitted-support generator and prove every generated support is listed or type-proved impossible.

Required outputs. boundaryscopemanifest, stratumincidencegraph, omittedsupportcertificate.

Minimal discharge. A deterministic manifest and graph contain every support and incidence relation; a rerun produces the same hash; an injected omitted support changes the residual from zero to nonzero.

Fail trigger. Any physical support, corner, junction, horizon, cut, localized sector, or gluing arrow is absent or discovered after a calculation.

Mandatory destructive controls. omitted fixed set; omitted codimension-two corner; state-dependent horizon injected after freeze.

Mapped gates. Black-hole-singularity, Gap-01, SG-1, SG-2, SG-3, SG-6, UQF-10, UQF-4, UQF-7, UQF-9.

BND-C02 — Covering/quotient and representation-picture equivalence

Owners: Boundary + Scale + Shape Legacy status: PRESERVED

Requirement. Publish an exact conversion between covering, quotient, interval, cut, doubled, orbifold, or equivalent pictures, including quotient order, volume factors, delta normalization, parity traces, orientation signs, field normalization, boundary measures, gauge restrictions, and global group data.

Thought experiment forcing the row. A factor-of-two error can leave qualitative spectra unchanged while changing anomaly density, normalization, and effective couplings. Agreement of labels is therefore insufficient.

Execution algorithm.

Choose one primary computation picture.
Derive every conversion factor from the group action and measures.
Reconstruct kernels, local densities, integrated actions, and gluing in a second picture.
Require exact equality after transport.

Required outputs. coverquotientconversion_packet.

Minimal discharge. Both pictures reproduce identical physical kernels and local/integrated densities after an explicit conversion table.

Fail trigger. An unexplained factor, sign, normalization, or global-group mismatch remains.

Mandatory destructive controls. factor-of-two delta weight; reversed normal orientation; wrong quotient gauge restriction.

Mapped gates. Gap-01, SG-1, SG-2, SG-3, SG-7, UQF-10, UQF-4, UQF-7, UQF-9.

BND-C03 — Lawful operator-domain and extension certificate

Owners: Boundary + Dynamics + Rulebook Legacy status: PRESERVED

Requirement. For every field, ghost, auxiliary, edge field, and load-bearing composite operator, define the complete domain: representation, parity, trace/boundary value, normal derivative or spectral condition, self-adjoint extension, ellipticity/strong ellipticity or hyperbolic admissibility, adjoint domain, gauge/BRST preservation, and kernel.

Thought experiment forcing the row. A formally symmetric operator may fail to be self-adjoint; a parity table may fail BRST preservation; two self-adjoint extensions may have different kernels. Thus boundary labels alone do not determine physics.

Execution algorithm.

Generate the candidate domain grammar before inspecting the gate target.
Compute the boundary form/Green identity.
Classify admissible extensions and gauge/ghost compatibility.
Test ellipticity, strong ellipticity, Fredholmness, or characteristic well-posedness by operator type.
Compute kernels and adjoint kernels on the frozen domain.

Required outputs. operatordomaincertificate, domainextensiongrammar, kernel_ledger.

Minimal discharge. Every operator has one frozen lawful domain with preserved gauge/BRST action and an explicit kernel; alternative admissible extensions receive dispositions.

Fail trigger. A parity or boundary-condition table substitutes for an operator domain, or an admissible extension is silently chosen after the desired spectrum is known.

Mandatory destructive controls. symmetric-not-self-adjoint domain; BRST image leaves domain; alternative extension changes zero-mode count.

Mapped gates. Black-hole-singularity, Gap-01, Gap-02, Gap-10/BG-10, Gap-11, Gap-13, SG-1, SG-2, SG-3, SG-5, SG-6, SG-7, SG-8, SG-9, UQF-10, UQF-14, UQF-3, UQF-4, UQF-5A/5B, UQF-7, UQF-9, theta-bar-QCD.

BND-C04 — Complete local anomaly polynomial at every stratum

Owners: Boundary Legacy status: PRESERVED

Requirement. At every anomaly-supporting stratum calculate the full local anomaly polynomial and descent in one declared convention, including projected bulk, localized fields, ghosts/measure, counterterms, nonabelian cubic, mixed, abelian, gravitational/local-Lorentz, and applicable higher-form terms.

Thought experiment forcing the row. The integrated anomaly can vanish while opposite fixed-set anomalies remain. A selected coefficient can vanish while another survives.

Execution algorithm.

Freeze the exact field/domain manifest and global charge normalization.
Generate all anomaly monomials allowed by dimension, symmetry, and tangential structure.
Calculate every source contribution at every stratum.
Record consistent/covariant convention and Bardeen–Zumino shifts.

Required outputs. localanomalypolynomial_packet.

Minimal discharge. Every applicable coefficient at every supporting stratum is calculated in a single convention from the shared manifest.

Fail trigger. Only an integrated anomaly or selected coefficient is shown, or different field/domain data are used.

Mandatory destructive controls. integrated-zero/local-nonzero; omitted mixed gravitational term; consistent/covariant mismatch.

Mapped gates. Gap-10/BG-10, SG-3, SG-4, UQF-4, UQF-7, theta-bar-QCD.

BND-C05 — Local anomaly-residual vector vanishes componentwise

Owners: Boundary + Dynamics Legacy status: PRESERVED

Requirement. Form the complete anomaly residual at each stratum from projected bulk, localized, ghost/measure, allowed counterterm, and inflow contributions; require the full vector of local residuals to vanish.

Thought experiment forcing the row. Two walls may carry equal and opposite anomalies. Their sum is zero, but local gauge invariance fails.

Execution algorithm.

Assemble each local contribution in the frozen convention.
Apply only predeclared lawful counterterms and inflow.
Calculate the residual vector, not merely its sum.
Run orientation and locality controls.

Required outputs. localanomalyresidual_vector.

Minimal discharge. The exact residual vector is zero at every fixed set, boundary, defect, interface, and corner where a local anomaly can live.

Fail trigger. Cancellation occurs only after integration or after fitting an unowned local term.

Mandatory destructive controls. opposite-wall cancellation; wrong orientation doubles one wall; missing corner anomaly.

Mapped gates. Gap-10/BG-10, SG-3, SG-4, UQF-4, UQF-7, theta-bar-QCD.

BND-C06 — Predeclared quantized inflow and counterterm provenance

Owners: Boundary + Scale + Dynamics Legacy status: PRESERVED

Requirement. Every inflow/counterterm action must identify its parent owner, support, form and trace normalization, coefficient provenance, quantization lattice, large-gauge behavior, orientation signs, local variation, metric/vacuum response, and microscopic versus matching status.

Thought experiment forcing the row. A real fitted coefficient can cancel a perturbative residual but fail under a large gauge transformation and has no predictive content.

Execution algorithm.

Generate allowed inflow terms from the frozen parent grammar.
Determine coefficient lattices before reading residuals.
Compute large-gauge phases and local variations.
Reject post-target or nonquantized fits.

Required outputs. quantizedinflowpacket.

Minimal discharge. Every inflow coefficient belongs to a derived/predeclared quantization lattice and passes all declared large-gauge and orientation tests.

Fail trigger. A coefficient is fitted after the residual is known, lies outside the lattice, or lacks parent provenance.

Mandatory destructive controls. unquantized fitted inflow; wrong-sign inflow; post-target counterterm.

Mapped gates. Gap-10/BG-10, SG-3, SG-4, UQF-4, UQF-7, theta-bar-QCD.

BND-C07 — Relative BV/BFV quantum-master completion

Owners: Boundary + Dynamics Legacy status: PRESERVED

Requirement. The field/ghost measure, boundary state, counterterms, anomaly and inflow must satisfy the relative quantum master equation or an explicitly equivalent quantum Ward identity and compose under gluing.

Thought experiment forcing the row. Classical BRST nilpotency can hold while the measure or boundary state carries a quantum anomaly.

Execution algorithm.

Construct bulk BV and boundary BFV data.
Verify domain preservation by gauge/ghost transformations.
Include measure determinants and anomaly terms.
Evaluate the relative QME and gluing composition.

Required outputs. boundarybvbfv_packet.

Minimal discharge. The relative QME residual is zero on the frozen domains and the boundary state composes into the closed-system quantum identity.

Fail trigger. Classical algebra closure is used while a measure/domain/boundary-state anomaly is uncomputed.

Mandatory destructive controls. classical-BRST/quantum-measure anomaly; ghost domain mismatch; QME gluing failure.

Mapped gates. Gap-13, SG-3, SG-4, UQF-14, UQF-3, UQF-4, UQF-5A/5B, UQF-5C, UQF-7, theta-bar-QCD.

BND-C08 — Correct global gauge form, charge lattice, and tangential target

Owners: Boundary + Shape Legacy status: PRESERVED

Requirement. Fix the actual global gauge group, quotient kernel, charge lattice, higher-form symmetry data, spin/pin/spin-c or other tangential structure, and the correct relative bordism/anomaly target.

Thought experiment forcing the row. The same Lie algebra can have different global anomalies and line operators for different global group forms.

Execution algorithm.

Derive the faithful global action from Actor charges.
Freeze tangential structures on all strata.
Construct the exact classifying target including quotient and one-form data.
Reject calculations performed only for the Lie algebra or a closed-bulk target when a relative target is required.

Required outputs. globalboundarytarget_packet.

Minimal discharge. The target used by eta/bordism/inflow calculations matches the faithful global group, charge lattice, and stratum tangential structures.

Fail trigger. The wrong quotient, charge lattice, tangential structure, or closed-bulk target is used.

Mandatory destructive controls. same Lie algebra/wrong global form; spin versus spin-c swap; closed-bulk target substituted for relative target.

Mapped gates. Gap-10/BG-10, SG-3, SG-4, UQF-4, UQF-7, theta-bar-QCD.

BND-C09 — Determinant/anomaly-line trivialization and cut-independent gluing

Owners: Boundary Legacy status: PRESERVED

Requirement. After local cancellation, construct and trivialize the determinant/anomaly line by Dai–Freed, APS, relative bordism, invertible-field theory, or an equivalent method; all declared mapping-torus/bordism phases must be unity and gluing must be cut-independent.

Thought experiment forcing the row. All perturbative polynomials may vanish while a global eta/bordism phase remains nontrivial.

Execution algorithm.

Construct the determinant/Pfaffian line over boundary data.
Evaluate declared mapping tori, fillings, or bordism generators.
Combine fermion, bulk invertible, counterterm, and inflow phases.
Test orientation reversal, cut independence, and associativity of gluing.

Required outputs. relativeglobalanomaly_packet.

Minimal discharge. A reproducible trivialization gives unit total phase on a generator-complete declared test set and obeys cut-independent gluing.

Fail trigger. Local anomalies vanish but the global phase is unknown/nontrivial, or gluing depends on the cut.

Mandatory destructive controls. local-zero/global-nontrivial; orientation reversal; nonassociative gluing.

Mapped gates. Gap-13, SG-3, SG-4, UQF-14, UQF-3, UQF-4, UQF-5C, UQF-7, theta-bar-QCD.

BND-C10 — Byte-identical shared boundary/domain manifest

Owners: Boundary + Shape + Dynamics + Granularity + Interdependence Legacy status: PRESERVED

Requirement. Chirality, family count, spectra, heat kernels, anomaly descent, stability, interactions, and Observer records must consume the same frozen field/parity/domain/support manifest and hashes.

Thought experiment forcing the row. A chirality calculation can use one parity table while an anomaly calculation silently uses another multiplicity or domain.

Execution algorithm.

Emit one canonical manifest.
Require every downstream packet to cite its hash.
Recompute all dependents on any manifest change.
Reject hash aliases and manual restatements.

Required outputs. sharedboundarymanifest, dependencyhashledger.

Minimal discharge. All boundary-dependent evidence cites the same canonical hash and stale dependents are automatically marked.

Fail trigger. Any downstream calculation uses different supports, fields, parities, domains, orientations, or multiplicities.

Mandatory destructive controls. chirality/anomaly parity mismatch; heat-kernel domain mismatch; stale hash accepted.

Mapped gates. Gap-01, Gap-10/BG-10, SG-10, SG-2, SG-3, SG-4, SG-5, SG-7, SG-8, SG-9, UQF-10, UQF-4, UQF-7, UQF-9, theta-bar-QCD.

BND-C11 — Boundary repair side-effect and backreaction audit

Owners: Boundary + Granularity + Vacuum + Dynamics + Interdependence Legacy status: PRESERVED

Requirement. Every boundary/domain/inflow repair must be audited for new light or edge modes, lost gauge symmetry, double counting, changed stress, vacuum terms, heat-kernel coefficients, rigidity, stability, interactions, causal flux, and Observer records.

Thought experiment forcing the row. A local anomaly can be canceled by adding a boundary field that creates an unwanted massless sector or vacuum stress.

Execution algorithm.

Diff all physical packets before and after the repair.
Re-run operator kernels, mode inventory, stress/vacuum, anomaly, interaction, and flux ledgers.
Classify every new effect with an owner.
Propagate stale hashes.

Required outputs. boundarysideeffect_packet.

Minimal discharge. Every changed physical effect is listed, owned, and revalidated; no hidden light mode, broken symmetry, or unowned stress remains.

Fail trigger. A repair is accepted without a full propagated physical diff.

Mandatory destructive controls. anomaly-canceling field creates zero mode; counterterm shifts vacuum stress; boundary repair breaks gauge symmetry.

Mapped gates. Black-hole-singularity, Gap-05-stability, Gap-05-value, Gap-11, Gap-13, Lambda-catastrophe, SG-1, SG-10, SG-3, SG-4, SG-5, SG-6, SG-8, SG-9, UQF-4, UQF-5A/5B, UQF-7, theta-bar-QCD.

BND-C12 — Machine reconstruction, support/domain exhaustion, and hostile controls

Owners: Boundary + Granularity + CSE Legacy status: PRESERVED

Requirement. A machine-reconstructible workflow must rebuild supports, domains, kernels, local/global anomalies, inflow, gluing, and controls; missing rows are UNKNOWN/OPEN, never zero.

Thought experiment forcing the row. A prose certificate can silently omit a stratum or default a missing anomaly row to zero.

Execution algorithm.

Serialize every packet with stable IDs and hashes.
Run schema validation and cross-packet referential-integrity checks.
Run the mandatory control suite.
Prove support/domain/inflow candidate exhaustion or report residuals.

Required outputs. integratedboundarycertificatev4, validationreport, control_results.

Minimal discharge. The validator reports zero missing required fields/references, all controls classify correctly, and every candidate row has a disposition.

Fail trigger. A control is misclassified, a missing row defaults to zero, or a candidate support/domain/inflow is unclassified.

Mandatory destructive controls. delete one stratum row; replace UNKNOWN with zero; omit one domain candidate.

Mapped gates. Black-hole-singularity, Born-rule, Gap-01, Gap-02, Gap-05-stability, Gap-13, Lambda-catastrophe, SG-1, SG-10, SG-2, SG-3, SG-4, SG-6, SG-7, UQF-10, UQF-14, UQF-3, UQF-4, UQF-5C, UQF-7, UQF-9, theta-bar-QCD.

BND-C13 — Variational boundary action, stress, reaction, and junction equations

Owners: Boundary + Dynamics + Vacuum Legacy status: NEW — FORCED BY ALL-GATE AUDIT

Requirement. The parent variational principle must include all boundary/corner terms needed for differentiability, define boundary canonical data and stress tensors, and publish reaction/junction equations for constrained or matched supports.

Thought experiment forcing the row. An operator may have a valid domain while the parent action is not differentiable; omitted Gibbons–Hawking-like or corner terms change stress and junction dynamics without changing the bulk equations.

Execution algorithm.

Vary the complete parent action including integration-by-parts terms.
Generate required boundary and corner actions from the frozen variational polarization.
Derive boundary stress, canonical momenta, junction/reaction equations, and conserved charges.
Test ordinary-source and vacuum-offset response.

Required outputs. boundaryvariationaljunction_packet.

Minimal discharge. The total action has a well-defined variation on the declared data; all boundary/corner equations and stresses are derived and solved or honestly OPEN.

Fail trigger. Bulk equations are used while uncanceled boundary variations, missing junction equations, or unowned boundary stress remain.

Mandatory destructive controls. omit required variational term; same bulk EOM/different boundary stress; junction source outside reaction span.

Mapped gates. Black-hole-singularity, Gap-01, Gap-05-stability, Gap-05-value, Gap-08, Gap-10/BG-10, Gap-11, Lambda-catastrophe, SG-1, SG-5, SG-6, SG-8, SG-9, UQF-10, UQF-14, UQF-4, UQF-5A/5B, UQF-5C, UQF-9, theta-bar-QCD.

BND-C14 — Time-dependent and moving-domain transport

Owners: Boundary + Dynamics + Time Synchronization Legacy status: NEW — FORCED BY ALL-GATE AUDIT

Requirement. For moving boundaries, evolving interfaces, topology-changing supports, or time-dependent domains, specify domain transport, corner compatibility, symplectic/probability flux, constraint propagation, and unitary or controlled open evolution.

Thought experiment forcing the row. A static self-adjoint domain can cease to define unitary evolution when the boundary moves; identical instantaneous spectra do not imply identical histories.

Execution algorithm.

Define the support worldvolume and synchronization class.
Construct a transport map between instantaneous domains.
Compute induced boundary work, particle/probability flux, and corner data.
Test composition, causality, and norm/constraint preservation over histories.

Required outputs. timedependentboundary_packet.

Minimal discharge. Domain transport is defined and composable; physical norm/constraints and all induced fluxes are accounted for across the claimed history.

Fail trigger. Static boundary data are reused for a moving/evolving support without a transport theorem.

Mandatory destructive controls. moving wall with static domain; topology change without corner packet; time-step composition failure.

Mapped gates. Black-hole-singularity, Gap-05-stability, Gap-08, Gap-10/BG-10, Gap-11, Gap-13, Lambda-catastrophe, SG-5, SG-6, UQF-10, UQF-14, UQF-5A/5B.

BND-C15 — Derived and state-dependent support realization

Owners: Boundary + Shape + Dynamics + Observer Legacy status: NEW — FORCED BY ALL-GATE AUDIT

Requirement. Causal/apparent horizons, phase interfaces, entangling cuts, coarse-graining cuts, and other solution- or state-dependent supports must be instantiated from SHP-X01 with induced geometry, normals, support equations, variation rules, accessibility, and dependency hashes.

Thought experiment forcing the row. Two states on the same Stage may differ by a horizon or phase wall carrying nonzero flux. Treating the support as absent loses physical records.

Execution algorithm.

Receive a derived-support packet from Shape/Dynamics.
Compute induced structure, orientation, incidence, and support equations.
Classify observer dependence and gauge invariance.
Feed the support into domain, edge, flux, anomaly, and gluing ledgers.

Required outputs. derivedsupportboundary_packet.

Minimal discharge. Every derived support in scope has a reproducible construction and is propagated to all boundary-dependent packets.

Fail trigger. A horizon/interface/cut is used in a claim but lacks a typed boundary realization or is treated as a fundamental Stage factor without proof.

Mandatory destructive controls. state-dependent horizon omitted; gauge-dependent apparent boundary counted as invariant; phase wall not propagated.

Mapped gates. Black-hole-singularity, Born-rule, Gap-08, Gap-10/BG-10, Gap-11, Gap-13, UQF-14, UQF-5A/5B.

BND-C16 — Corner, junction, incidence, and multi-interface composition

Owners: Boundary + Dynamics + Interdependence Legacy status: NEW — FORCED BY ALL-GATE AUDIT

Requirement. All codimension-two-or-higher corners, intersecting defects, junctions, and multi-interface compositions must have compatible incidence, orientation, matching/transmission conditions, corner actions, anomaly terms, and associative gluing.

Thought experiment forcing the row. Pairwise boundary conditions can each pass while their intersection is inconsistent or carries an uncanceled corner anomaly.

Execution algorithm.

Close the stratum incidence graph under intersections.
Derive compatibility and transmission conditions at each junction.
Calculate corner variations, charges, edge modes, and anomaly descent.
Test associativity under different gluing orders.

Required outputs. cornerjunctionpacket.

Minimal discharge. Every incidence cell has compatible matching data and all multi-step gluings give equivalent results.

Fail trigger. A corner/junction is omitted, over/underdetermined, anomalous, or gluing-order dependent.

Mandatory destructive controls. pairwise-pass/corner-fail; junction orientation cycle; nonassociative three-piece gluing.

Mapped gates. Black-hole-singularity, Gap-13, SG-1, SG-5, SG-6, UQF-10, UQF-14, UQF-4.

BND-C17 — Regional algebras, edge modes, factorization, and entanglement cuts

Owners: Boundary + Dynamics + Observer + Granularity Legacy status: NEW — FORCED BY ALL-GATE AUDIT

Requirement. For gauge/gravitational subsystems and cuts, construct the regional observable algebra, center/superselection data, edge-mode completion, factorization or extended-Hilbert-space map, entropy/information records, and gluing back to the global physical space.

Thought experiment forcing the row. A global gauge-invariant Hilbert space need not factorize across a cut; ignoring edge modes can produce false entropy loss or nonunitarity.

Execution algorithm.

Define the cut/support and regional gauge group.
Construct regional algebras and centers.
Add only required edge variables with Actor/Co-Actor dispositions.
Build the factorization/gluing map and information-flow ledger.
Test cut independence of global predictions.

Required outputs. regionaledgefactorization_packet.

Minimal discharge. The regional algebra and edge completion reproduce the global physical space under gluing and yield finite Observer-accessible records.

Fail trigger. Naive tensor factorization is assumed, edge sectors are omitted/double-counted, or subsystem loss is called global nonunitarity.

Mandatory destructive controls. Gauss-law factorization failure; edge-mode double count; cut-dependent global probability.

Mapped gates. Black-hole-singularity, Born-rule, Gap-02, Gap-08, Gap-13, UQF-14, UQF-3.

BND-C18 — Causal, null, horizon, and asymptotic boundary data with flux balance

Owners: Boundary + Dynamics + Time Synchronization + Observer Legacy status: NEW — FORCED BY ALL-GATE AUDIT

Requirement. Classify spacelike, timelike, null, characteristic, horizon, and asymptotic components; specify admissible data, radiation/absorbing/reflection conditions, causal support, symplectic/charge/energy/probability/information flux, and asymptotic charges/memory where applicable.

Thought experiment forcing the row. A local conservation law can hold while unaccounted flux crosses a horizon or null infinity; imposing timelike data on a characteristic surface can overdetermine evolution.

Execution algorithm.

Classify causal type and induced/degenerate geometry.
Select data compatible with the PDE characteristic structure.
Compute all boundary currents and charges.
Establish synchronization and Observer record maps.
Verify global balance after adding all interfaces/asymptotic pieces.

Required outputs. causalasymptoticboundary_packet.

Minimal discharge. The initial-boundary problem is causally admissible and every regional/global current balances including horizon/asymptotic flux.

Fail trigger. Boundary data are incompatible with causal type, or a flux channel is omitted.

Mandatory destructive controls. horizon flux omitted; null boundary overdetermined; absorbing condition violates gauge constraint.

Mapped gates. Black-hole-singularity, Born-rule, Gap-02, Gap-05-stability, Gap-05-value, Gap-08, Gap-10/BG-10, Gap-11, Gap-13, Lambda-catastrophe, UQF-14, UQF-3, UQF-5A/5B, UQF-5C.

Owners: Boundary + Dynamics + Granularity + Scale Legacy status: NEW — FORCED BY ALL-GATE AUDIT

Requirement. Boundary conditions, counterterms, edge sectors, heat-kernel coefficients, anomalies, and spectra must remain controlled under regulator/scheme changes, operator-basis enlargement, cutoff/tower refinement, and allowed boundary RG flow.

Thought experiment forcing the row. A domain can be self-adjoint at tree level but generate new boundary operators or lose strong ellipticity under renormalization; a finite a6 calculation does not prove all-order consistency.

Execution algorithm.

Generate all boundary operators/counterterms allowed by the frozen grammar.
Compute heat-kernel and loop divergences on the exact domain.
Track domain/coupling flow and regulator family.
Run nested refinement in modes, strata, derivative order, and schemes.
Require convergence or state an honest scope ceiling.

Required outputs. boundaryrefinementpacket, heatkernelboundary_packet.

Minimal discharge. All generated boundary terms are owned; regulator/scheme/refinement variation is quantified; the claim is limited to the certified scope with a tail theorem for global claims.

Fail trigger. A finite-order/domain-specific result is promoted globally, or generated boundary operators are omitted.

Mandatory destructive controls. new boundary counterterm under loop; loss of strong ellipticity; fixed point disappears under boundary-basis refinement.

Mapped gates. Gap-01, Gap-02, Gap-05-stability, Gap-05-value, Gap-08, Gap-10/BG-10, Gap-11, Gap-13, Lambda-catastrophe, SG-1, SG-10, SG-3, SG-4, SG-5, SG-6, SG-7, SG-8, SG-9, UQF-10, UQF-14, UQF-3, UQF-4, UQF-5A/5B, UQF-5C, UQF-7, UQF-9, theta-bar-QCD.

BND-C20 — Candidate-neutral boundary/domain/inflow grammar and provenance exhaustion

Owners: Boundary + CSE + Granularity + Interdependence Legacy status: NEW — FORCED BY ALL-GATE AUDIT

Requirement. Before outcomes are inspected, generate the complete lawful grammar of support realizations, boundary conditions/extensions, localized sectors, counterterms, inflow actions, gluing polarizations, and repair rights; canonicalize physical duplicates and exhaust the grammar.

Thought experiment forcing the row. Choosing parity, extension, localized matter, or inflow only after seeing the desired spectrum/anomaly is target loading even when each chosen object is mathematically lawful.

Execution algorithm.

Freeze generation rules and provenance classes.
Enumerate finite candidates or prove a class theorem/finiteness result.
Canonicalize exact duplicates using Granularity.
Apply equal completion rights and witness standards.
Run omitted-rival and post-target-repair controls.

Required outputs. boundarycandidategrammar, boundaryexhaustioncertificate.

Minimal discharge. Every lawful candidate class has one disposition and one provenance; omitted-rival controls detect deleted candidates; no post-target repair is present.

Fail trigger. The preferred boundary condition/inflow/edge sector is selected after the target is known or a lawful rival is unclassified.

Mandatory destructive controls. post-target parity choice; preferred candidate gets unique localized field; omitted extension rival.

Mapped gates. Black-hole-singularity, Born-rule, Gap-01, Gap-02, Gap-05-stability, Gap-05-value, Gap-08, Gap-10/BG-10, Gap-11, Gap-13, Lambda-catastrophe, SG-1, SG-10, SG-2, SG-3, SG-4, SG-5, SG-6, SG-7, SG-8, SG-9, UQF-10, UQF-14, UQF-3, UQF-4, UQF-5A/5B, UQF-5C, UQF-7, UQF-9, theta-bar-QCD.

6. Boundary compilation pipeline

The gate execution order is mandatory:

\[ \text{Shape supports} \to \text{Boundary support/incidence closure} \to \text{variational and operator domains} \to \text{kernels/edge sectors} \to \text{local anomaly vector} \to \text{quantized inflow} \to \text{global anomaly line/QME/gluing} \to \text{causal/regional flux} \to \text{refinement and side effects}. \]

Later stages cannot repair an earlier failed domain by arithmetic. A global phase cannot validate an invalid local domain. A boundary counterterm cannot be introduced after the target residual is known unless it was generated by the frozen candidate grammar.

6.1 Support and incidence saturation

Generate all fundamental and derived supports, close under intersections and history, and iterate until no new support, corner, junction, orientation, or gluing arrow appears.

6.2 Domain and variational saturation

For every operator/support pair, generate lawful extensions and variational polarizations before target inspection. Compute boundary forms, kernels, stresses, junction equations, and gauge/BRST preservation.

6.3 Quantum boundary saturation

Generate all local anomaly classes, allowed counterterms/inflow, global targets, determinant-line tests, QME terms, edge sectors, and gluing compositions. Iterate until no new in-grammar quantum boundary object appears.

6.4 History, regional, and refinement saturation

Generate time-dependent supports, domain transports, causal/asymptotic data, regional algebras, edge modes, flux channels, boundary counterterms, regulator families, and refinement directions.

7. Integrated certificate schema

integrated_boundary_certificate_v4:
  gate_id:
  candidate_id:
  branch_id:
  authority_hashes:
  selected_rows:
  scope_manifest:
  incidence_graph:
  shared_boundary_manifest_hash:
  operator_domains:
  variational_and_junction_packets:
  kernels_and_edge_modes:
  local_anomaly_packets:
  local_residual_vector:
  inflow_packets:
  global_target:
  determinant_line_and_gluing:
  bv_bfv_qme:
  dynamic_support_packets:
  regional_factorization_packets:
  causal_asymptotic_packets:
  refinement_packets:
  side_effect_audit:
  negative_controls:
  boundary_residual_vector:
  claim_ceiling:
  physical_terminal:
  project_dependency_terminal:
  evidence_hashes:
  reopen_triggers:

8. Boundary residual vector and closure

Define

\[ \mathcal R{\rm BND}=(r1,\ldots,r_{20}), \]

where $r_i$ is the count or quantified norm of unresolved items for BND-Ci. A scoped positive Boundary terminal requires every selected hard row to PASS and its residual to vanish. Rows may be NOT-APPLICABLE only by a type proof. Missing evidence is OPEN, never zero.

A gate's claim ceiling is the weakest selected Boundary row. In particular:

BND-A/domain PASS does not imply BND-B/global quantum PASS;
local anomaly-vector zero does not imply determinant-line trivialization;
static-domain PASS does not imply moving-domain PASS;
global conservation does not imply regional/horizon flux closure;
one domain survivor does not imply candidate-grammar exhaustion.

9. Status grammar

PASS — the named witness meets the minimal discharge.
FAIL — a reproducible counterexample or failed control exists.
OPEN — required evidence is missing, incomplete, or inconclusive.
NOT-EVALUATED — an earlier hard failure stopped execution.
NOT-APPLICABLE — a type proof establishes impossibility of application.
CONSTRUCTION-ANCHOR — a declared boundary/domain/inflow object realizes the result but is not derived.
CONDITIONAL-ON-BND-A — domain/kernel closure is owed.
CONDITIONAL-ON-BND-B — local/global anomaly, QME, or gluing closure is owed.
RESTART-REQUIRED — a frozen support, domain, field, group, regulator, or inflow changed.
EXTERNAL-WALL — the complete Boundary method is defined but a necessary external theorem/calculation is unavailable.

10. Universal anti-promotion rules

A notation such as S1/Z2 is not a stratum inventory.
A parity table is not an operator-domain certificate.
A symmetric operator is not automatically self-adjoint.
A static lawful domain is not automatically lawful for a moving boundary.
Integrated anomaly cancellation is not local cancellation.
Local polynomial cancellation is not global anomaly-line trivialization.
A fitted inflow coefficient is not a quantized parent relation.
Classical BRST closure is not a relative quantum-master certificate.
Global Hilbert-space unitarity is not subsystem factorization.
Local conservation is not regional/horizon/asymptotic flux closure.
A finite heat-kernel coefficient is not all-order boundary consistency.
One tested boundary condition is not a selected boundary condition without grammar exhaustion.
An inaccessible boundary record is not absent without a type proof.
A boundary repair is not neutral until spectra, stress, vacuum, rigidity, interactions, and records are rerun.

11. All-gate execution profiles

Black-hole-singularity

Source terminal: DISSOLVED-GIVEN-root / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C03, BND-C11, BND-C12, BND-C13, BND-C14, BND-C15, BND-C16, BND-C17, BND-C18, BND-C20. Gate discipline: Derived horizons/interiors and causal regional boundaries are load-bearing; dissolving a continuum singularity does not remove flux, domain, or information obligations. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Born-rule

Source terminal: CLOSED / CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: CONDITIONAL/SCOPED Selected rows: BND-C12, BND-C15, BND-C17, BND-C18, BND-C20. Gate discipline: Boundary is conditional through subsystem/measurement cuts; a type proof may mark rows N/A only when no regional factorization enters the claim. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Gap-01

Source terminal: DERIVED-GIVEN-anchor / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C02, BND-C03, BND-C10, BND-C12, BND-C13, BND-C19, BND-C20. Gate discipline: The order-six coefficient is domain- and boundary-condition-dependent and cannot be certified without exact BND-A and refinement packets. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Gap-02

Source terminal: CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: CONDITIONAL/SCOPED Selected rows: BND-C03, BND-C12, BND-C17, BND-C18, BND-C19, BND-C20. Gate discipline: Finite-volume, asymptotic, and regional boundary choices must be shown not to manufacture the mass gap. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Gap-05-stability

Source terminal: CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C11, BND-C12, BND-C13, BND-C14, BND-C18, BND-C19, BND-C20. Gate discipline: Boundary counterterms, stresses, moving cosmological supports, and renormalization can alter vacuum response. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Gap-05-value

Source terminal: MEASURED-ANCHOR / RESOLVED +0 Boundary role: CONDITIONAL/SCOPED Selected rows: BND-C11, BND-C13, BND-C18, BND-C19, BND-C20. Gate discipline: Measured vacuum response must include boundary stress/counterterm contributions at the declared scope. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Gap-08

Source terminal: DISSOLVED-GIVEN-root / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C13, BND-C14, BND-C15, BND-C17, BND-C18, BND-C19, BND-C20. Gate discipline: Initial surfaces, horizons, and asymptotic records are load-bearing for perturbation spectra. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Gap-10/BG-10

Source terminal: CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C03, BND-C04, BND-C05, BND-C06, BND-C08, BND-C10, BND-C13, BND-C14, BND-C15, BND-C18, BND-C19, BND-C20. Gate discipline: Phase walls, chiral domains, anomaly transport, and nonequilibrium boundary flux can change production and washout. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Gap-11

Source terminal: CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C03, BND-C11, BND-C13, BND-C14, BND-C15, BND-C18, BND-C19, BND-C20. Gate discipline: Portal production/decay may depend on phase interfaces, localized operators, and asymptotic flux. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Gap-13

Source terminal: CLOSED / PROJECT-DEPENDENCY / CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C03, BND-C07, BND-C09, BND-C11, BND-C12, BND-C14, BND-C15, BND-C16, BND-C17, BND-C18, BND-C19, BND-C20. Gate discipline: Page/microstate claims require regional algebra, edge modes, horizon cuts, global phases, and information flux. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

Lambda-catastrophe

Source terminal: DISSOLVED-GIVEN-root / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C11, BND-C12, BND-C13, BND-C14, BND-C18, BND-C19, BND-C20. Gate discipline: Boundary stress, counterterms, and history-dependent supports must not reintroduce the offset. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-1

Source terminal: CLOSED / DERIVED-GIVEN-SHAPE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C02, BND-C03, BND-C11, BND-C12, BND-C13, BND-C16, BND-C19, BND-C20. Gate discipline: Geometry selection includes lawful boundary/domain grammar, variational completion, corner consistency, and candidate exhaustion. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-10

Source terminal: DERIVED-GIVEN-anchor / RESOLVED +0 Boundary role: CONDITIONAL/SCOPED Selected rows: BND-C10, BND-C11, BND-C12, BND-C19, BND-C20. Gate discipline: Scope consistency requires shared hashes, refinement ceilings, and no hidden boundary candidate. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-2

Source terminal: CLOSED / CERTIFIED-IRREDUCIBLE-CATEGORY-FLOOR / RESOLVED +0 Boundary role: CONDITIONAL/SCOPED Selected rows: BND-C01, BND-C02, BND-C03, BND-C10, BND-C12, BND-C20. Gate discipline: Gauge zero modes require exact domains, quotient normalization, and no omitted boundary/edge carrier. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-3

Source terminal: DERIVED-GIVEN-E / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C02, BND-C03, BND-C04, BND-C05, BND-C06, BND-C07, BND-C08, BND-C09, BND-C10, BND-C11, BND-C12, BND-C19, BND-C20. Gate discipline: Unconditional chirality requires one domain manifest and complete local/global anomaly closure. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-4

Source terminal: CLOSED / DERIVED-GIVEN-E / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C04, BND-C05, BND-C06, BND-C07, BND-C08, BND-C09, BND-C10, BND-C11, BND-C12, BND-C19, BND-C20. Gate discipline: Charge/anomaly closure requires the faithful global target, local fixed-set vector, quantized inflow, and determinant-line trivialization. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-5

Source terminal: DERIVED-GIVEN-anchor / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C03, BND-C10, BND-C11, BND-C13, BND-C14, BND-C16, BND-C19, BND-C20. Gate discipline: Electroweak/Wilson realization may depend on boundary conditions, localized terms, junctions, and their radiative stability. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-6

Source terminal: DERIVED-GIVEN-anchor / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C03, BND-C11, BND-C12, BND-C13, BND-C14, BND-C16, BND-C19, BND-C20. Gate discipline: Moduli include interval, boundary-position, localized-sector, and domain deformations. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-7

Source terminal: DISSOLVED-GIVEN-root / RESOLVED +0 Boundary role: CONDITIONAL/SCOPED Selected rows: BND-C02, BND-C03, BND-C10, BND-C12, BND-C19, BND-C20. Gate discipline: Thresholds require exact normalization, domains, tower/edge inventory, and boundary refinement. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-8

Source terminal: CLOSED / RESCUED / DISSOLVED-WRONG-RULER + DERIVED-GIVEN-13D-ACTOR / RESOLVED +0 Boundary role: CONDITIONAL/SCOPED Selected rows: BND-C03, BND-C10, BND-C11, BND-C13, BND-C19, BND-C20. Gate discipline: Flavor overlaps and masses require the same domains and all localized interaction terms. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

SG-9

Source terminal: DERIVED-GIVEN-anchor / RESOLVED +0 Boundary role: CONDITIONAL/SCOPED Selected rows: BND-C03, BND-C10, BND-C11, BND-C13, BND-C19, BND-C20. Gate discipline: Dangerous operators may be boundary-localized or generated by boundary renormalization. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

UQF-10

Source terminal: RESOLVED +0 / DERIVED-GIVEN-anchor + CLOSED-NEGATIVE leg Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C02, BND-C03, BND-C10, BND-C12, BND-C13, BND-C14, BND-C16, BND-C19, BND-C20. Gate discipline: Compactification consistency includes all strata, domains, junctions, and domain/refinement rivals. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

UQF-14

Source terminal: CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C03, BND-C07, BND-C09, BND-C12, BND-C13, BND-C14, BND-C15, BND-C16, BND-C17, BND-C18, BND-C19, BND-C20. Gate discipline: Unitarity/causality claims require lawful causal boundaries, edge factorization, gluing, and flux balance. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

UQF-3

Source terminal: CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C03, BND-C07, BND-C09, BND-C12, BND-C17, BND-C18, BND-C19, BND-C20. Gate discipline: Reflection positivity/continuation depends on domains, global phases, regional algebra, and regulator stability. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

UQF-4

Source terminal: CLOSED / DERIVED-GIVEN-13D-SHAPE / GLOBAL-ANOMALY-CONSISTENT / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C02, BND-C03, BND-C04, BND-C05, BND-C06, BND-C07, BND-C08, BND-C09, BND-C10, BND-C11, BND-C12, BND-C13, BND-C16, BND-C19, BND-C20. Gate discipline: Boundary B is decisive: local/global anomaly, QME, determinant line, and gluing must all pass. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

UQF-5A/5B

Source terminal: CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C03, BND-C07, BND-C11, BND-C13, BND-C14, BND-C15, BND-C18, BND-C19, BND-C20. Gate discipline: Graviton propagation and positivity depend on variational boundary terms, causal data, horizons, and regulator-stable domains. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

UQF-5C

Source terminal: CLOSED / CERTIFIED-IRREDUCIBLE-FLOOR / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C07, BND-C09, BND-C12, BND-C13, BND-C18, BND-C19, BND-C20. Gate discipline: Any constructive UV claim must include all generated boundary operators, global phases, and refinement stability. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

UQF-7

Source terminal: DERIVED-GIVEN-anchor / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C02, BND-C03, BND-C04, BND-C05, BND-C06, BND-C07, BND-C08, BND-C09, BND-C10, BND-C11, BND-C12, BND-C19, BND-C20. Gate discipline: The AD-1 chiral-domain result remains conditional on the shared BND-A/B certificate for unconditional quantum closure. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

UQF-9

Source terminal: CERTIFIED-IRREDUCIBLE / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C01, BND-C02, BND-C03, BND-C10, BND-C12, BND-C13, BND-C19, BND-C20. Gate discipline: Heat-kernel/UV coefficients require exact boundary domains, variational terms, and refinement/tail control. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

theta-bar-QCD

Source terminal: DISSOLVED-GIVEN-root / RESOLVED +0 Boundary role: LOAD-BEARING Selected rows: BND-C03, BND-C04, BND-C05, BND-C06, BND-C07, BND-C08, BND-C09, BND-C10, BND-C11, BND-C12, BND-C13, BND-C19, BND-C20. Gate discipline: Topological relaxation and axion/top-form mechanisms require faithful global targets, quantized boundary terms, and anomaly-line consistency. Claim ceiling: No gate terminal may exceed the weakest required Boundary row. Missing evidence is OPEN; a type proof is required for NOT-APPLICABLE.

12. Mandatory hostile-review suite

TE-BND-01 — BND-C01

Counterexample: Two candidates can share the same bulk manifold and action while differing by one omitted fixed component carrying a localized kernel or anomaly. Bulk equality therefore does not determine the physical boundary object. Injected control: omitted fixed set Expected: FAIL if the candidate lacks BND-C01 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-02 — BND-C02

Counterexample: A factor-of-two error can leave qualitative spectra unchanged while changing anomaly density, normalization, and effective couplings. Agreement of labels is therefore insufficient. Injected control: factor-of-two delta weight Expected: FAIL if the candidate lacks BND-C02 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-03 — BND-C03

Counterexample: A formally symmetric operator may fail to be self-adjoint; a parity table may fail BRST preservation; two self-adjoint extensions may have different kernels. Thus boundary labels alone do not determine physics. Injected control: symmetric-not-self-adjoint domain Expected: FAIL if the candidate lacks BND-C03 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-04 — BND-C04

Counterexample: The integrated anomaly can vanish while opposite fixed-set anomalies remain. A selected coefficient can vanish while another survives. Injected control: integrated-zero/local-nonzero Expected: FAIL if the candidate lacks BND-C04 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-05 — BND-C05

Counterexample: Two walls may carry equal and opposite anomalies. Their sum is zero, but local gauge invariance fails. Injected control: opposite-wall cancellation Expected: FAIL if the candidate lacks BND-C05 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-06 — BND-C06

Counterexample: A real fitted coefficient can cancel a perturbative residual but fail under a large gauge transformation and has no predictive content. Injected control: unquantized fitted inflow Expected: FAIL if the candidate lacks BND-C06 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-07 — BND-C07

Counterexample: Classical BRST nilpotency can hold while the measure or boundary state carries a quantum anomaly. Injected control: classical-BRST/quantum-measure anomaly Expected: FAIL if the candidate lacks BND-C07 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-08 — BND-C08

Counterexample: The same Lie algebra can have different global anomalies and line operators for different global group forms. Injected control: same Lie algebra/wrong global form Expected: FAIL if the candidate lacks BND-C08 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-09 — BND-C09

Counterexample: All perturbative polynomials may vanish while a global eta/bordism phase remains nontrivial. Injected control: local-zero/global-nontrivial Expected: FAIL if the candidate lacks BND-C09 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-10 — BND-C10

Counterexample: A chirality calculation can use one parity table while an anomaly calculation silently uses another multiplicity or domain. Injected control: chirality/anomaly parity mismatch Expected: FAIL if the candidate lacks BND-C10 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-11 — BND-C11

Counterexample: A local anomaly can be canceled by adding a boundary field that creates an unwanted massless sector or vacuum stress. Injected control: anomaly-canceling field creates zero mode Expected: FAIL if the candidate lacks BND-C11 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-12 — BND-C12

Counterexample: A prose certificate can silently omit a stratum or default a missing anomaly row to zero. Injected control: delete one stratum row Expected: FAIL if the candidate lacks BND-C12 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-13 — BND-C13

Counterexample: An operator may have a valid domain while the parent action is not differentiable; omitted Gibbons–Hawking-like or corner terms change stress and junction dynamics without changing the bulk equations. Injected control: omit required variational term Expected: FAIL if the candidate lacks BND-C13 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-14 — BND-C14

Counterexample: A static self-adjoint domain can cease to define unitary evolution when the boundary moves; identical instantaneous spectra do not imply identical histories. Injected control: moving wall with static domain Expected: FAIL if the candidate lacks BND-C14 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-15 — BND-C15

Counterexample: Two states on the same Stage may differ by a horizon or phase wall carrying nonzero flux. Treating the support as absent loses physical records. Injected control: state-dependent horizon omitted Expected: FAIL if the candidate lacks BND-C15 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-16 — BND-C16

Counterexample: Pairwise boundary conditions can each pass while their intersection is inconsistent or carries an uncanceled corner anomaly. Injected control: pairwise-pass/corner-fail Expected: FAIL if the candidate lacks BND-C16 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-17 — BND-C17

Counterexample: A global gauge-invariant Hilbert space need not factorize across a cut; ignoring edge modes can produce false entropy loss or nonunitarity. Injected control: Gauss-law factorization failure Expected: FAIL if the candidate lacks BND-C17 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-18 — BND-C18

Counterexample: A local conservation law can hold while unaccounted flux crosses a horizon or null infinity; imposing timelike data on a characteristic surface can overdetermine evolution. Injected control: horizon flux omitted Expected: FAIL if the candidate lacks BND-C18 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-19 — BND-C19

Counterexample: A domain can be self-adjoint at tree level but generate new boundary operators or lose strong ellipticity under renormalization; a finite a6 calculation does not prove all-order consistency. Injected control: new boundary counterterm under loop Expected: FAIL if the candidate lacks BND-C19 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

TE-BND-20 — BND-C20

Counterexample: Choosing parity, extension, localized matter, or inflow only after seeing the desired spectrum/anomaly is target loading even when each chosen object is mathematically lawful. Injected control: post-target parity choice Expected: FAIL if the candidate lacks BND-C20 Why irreducible: The old/lower-dimensional description can pass while the physical result changes; the row is therefore independently load-bearing within the current gate corpus.

13. Gate execution procedure

Read START_HERE.md, this authority, the gate contract, and the current Shape/Granularity/Dynamics hashes.
Mask the expected answer and historical terminal from calculation code.
Select Boundary rows from the all-gate crosswalk and add any gate-specific rows forced by type.
Freeze supports, domain grammar, global group, tangential structure, regulator, boundary conditions, inflow candidate grammar, Observer, and Scale.
Run an immutable audit row by row. Missing evidence is OPEN.
Freeze failures before any repair.
Propose only reusable repairs; rerun all mapped gates conceptually and propagate hashes.
Execute all mandatory controls and the machine validator.
Emit physical result, Boundary sufficiency result, project dependency, claim ceiling, residual vector, evidence hashes, and reopen triggers separately.
Never manually declare the gate closed; hand evidence to the status engine.

14. Ratification conditions

BB-BND-4.0 may become controlling only after: exact legacy preservation passes; all packet schemas validate; all twenty thought experiments classify correctly; target-masked calibration on SG-3, SG-4, UQF-7, and UQF-4 does not overclose; hostile review finds no omitted all-gate Boundary capability; and all dependent gates receive new authority hashes.

14A. V4.1 operational-completeness and preservation theorem

V4.1 changes no physical Boundary row and weakens no V4.0 or legacy obligation. It repairs the execution package so that every output named by BND-C01 through BND-C20 has a machine-readable schema, empty template, owner mapping, validation rule, and evidence-directory location.

Let $\mathcal O{m req}$ be the set of all output identifiers named by the twenty constraint rows, and let $\mathcal S{m pkt}$ be the set of packet schemas in the controlling registry. Operational completeness requires

\[ \mathcal O{m req}\subseteq\mathcal S{m pkt},\qquad N_{m schema-missing}=0. \]

The package validator must additionally prove:

exact SHA-256 preservation of BB-BND-4.0, BB-BND-A-1, BB-BND-B-1, and BB-AD-1;
verbatim inclusion of all three legacy authorities in this standalone authority;
semantic parity of CSV and JSON constraint/gate registries;
twenty unique sequential constraint IDs and thirty unique gate profiles;
every selected gate row refers to a defined constraint and every constraint is used by at least one gate;
every required output has a field registry, JSON Schema definition, empty template, and constraint-owner map;
every internal file reference in START_HERE, README, and the execution prompt resolves;
all JSON parses, all checksums verify, and all destructive controls classify as expected;
historical source_terminal values remain metadata only and are never read as target evidence;
no gate verdict exceeds the weakest selected Boundary row.

The preservation residual is

\[ \mathcal R{m BND-pres}= (N{m source-mismatch},N{m unmapped-old},N{m weakened},N{m schema-missing},N{m broken-ref},N{m registry-mismatch},N{m control-fail}). \]

A V4.1 package is valid only if $\mathcal R_{m BND-pres}=0$.

14B. Complete evidence contract

For a gate selecting row set $Rg$, the execution agent SHALL emit every packet named by the outputs field of every row in $Rg$, plus dependencyhashledger, controlresults, validationreport, and integratedboundarycertificate_v4. A packet may be omitted only when the row is adjudicated NOT-APPLICABLE by a frozen type proof; the proof itself must be recorded in the integrated certificate.

Required evidence directory:

BOUNDARY_EVIDENCE/<gate_id>/
  00_GATE_CONTRACT/
  01_AUTHORITY_HASHES/
  02_SUPPORT_AND_INCIDENCE/
  03_DOMAINS_KERNELS_VARIATION/
  04_LOCAL_ANOMALY/
  05_INFLOW_GLOBAL_QME_GLUING/
  06_DYNAMIC_REGIONAL_CAUSAL/
  07_REFINEMENT_EXHAUSTION/
  08_CONTROLS/
  09_CERTIFICATE_AND_STATUS/

The controlling machine contracts are 02REGISTRIES/BOUNDARYPACKETFIELDREGISTRYV41.json, 02REGISTRIES/BOUNDARYPACKETBUNDLEJSONSCHEMAV41.json, and 02REGISTRIES/BOUNDARYOUTPUTTOCONSTRAINTMAPV41.json.

Appendix A — Exact BB-BND-A-1 source (verbatim)

--- title: "BB-BND-A-1 — Fixed-Set Inventory and Operator-Domain Completion" buildingblockid: "BB-BND-A-1" version: "1.0" date: "2026-07-24" status: "MACHINERY-COMPLETE DEVELOPMENT AUTHORITY — NOT FROZEN" scope: "Split boundary authority under package v3.3.2" protocolfreeze: false canonicalratification: false packageauthorityversion: "3.3.2" ---

BB-BND-A-1 — Fixed-Set Inventory and Operator-Domain Completion

0. Status

MACHINERY-COMPLETE DEVELOPMENT AUTHORITY.
CANDIDATE-SPECIFIC DOMAIN EXECUTION OWED.
DOES NOT CLAIM ANOMALY/INFLOW CLOSURE.

1. Owned problem

Given a quotient, orbifold, boundary, defect, or interface, construct the complete stratified physical object and a lawful operator domain before any chirality, anomaly, heat-kernel, or inflow calculation.

2. Stratified inventory

For every component publish:

regular bulk stratum;
fixed set/boundary/corner ID;
dimension and isotropy group;
normal representation and orientation;
restricted global gauge group;
localized fields;
edge variables;
allowed gauge transformations;
gluing partners;
observer accessibility.

A notation such as $S^1/\mathbb Z_2$ is not an inventory.

3. Covering-to-quotient conversion

Choose a primary picture and publish the conversion table:

quotient order;
bulk-volume factor;
fixed-point delta normalization;
parity trace;
normal orientation;
gauge-transformation restriction;
field normalization;
boundary measure.

The covering and interval descriptions must reproduce identical kernels and local densities.

4. Operator-domain construction

For every bulk field, localized field, and ghost, specify:

representation and global charge;
parity at each fixed set;
boundary value and normal derivative condition;
self-adjoint extension;
ellipticity/strong ellipticity where required;
gauge/BRST preservation;
zero-mode kernel;
adjoint-domain compatibility.

A parity table without these rows fails.

5. Shared chirality/domain manifest

The byte-identical manifest must feed:

chiral zero-mode calculation;
family count;
localized anomaly calculation;
heat-kernel coefficients;
boundary spectrum;
stability analysis.

Until BND-A passes, chirality is CONDITIONAL-ON-BND-A.

6. Finite execution algorithm

enumerate strata;
generate field/parity/domain rows;
construct each kinetic/operator domain;
test self-adjointness and ellipticity;
test gauge and BRST preservation;
enumerate kernels and edge modes;
compare cover and quotient outputs;
emit manifest and hashes.

7. Certificate

fixed_set_domain_certificate:
  candidate_id:
  branch_id:
  cover:
  quotient:
  conversion_table:
  strata:
  fields_and_ghosts:
  operator_domains:
  self_adjointness:
  ellipticity:
  gauge_brst_preservation:
  kernels:
  edge_modes:
  chirality_manifest_hash:
  heat_kernel_manifest_hash:
  evidence_hashes:
  verdict:

8. Negative controls

omitted fixed set;
reversed normal orientation;
odd zero mode incorrectly retained;
anomaly arithmetic on a non-BRST-preserving domain;
cover/quotient factor-of-two mismatch;
boundary condition that is symmetric but not self-adjoint;
domain change not propagated to chirality.

9. Terminal

BND-A PASS:
  COMPLETE STRATIFIED INVENTORY /
  LAWFUL OPERATOR DOMAIN /
  COVER-QUOTIENT CONSISTENCY.

BND-B:
  STILL REQUIRED FOR QUANTUM ANOMALY/INFLOW CLOSURE.

Owned hard constraints and acceptance evidence

The full controlling registry is EVIDENCEDISCHARGEREGISTRYV33_2.md. The rows below are embedded because this block owns or directly co-owns them.

| ID | Required witness | Minimal discharge | Fail trigger | |---|---|---|---| | SHP-C03 | Dirac/kernel computation using the shared domain manifest | The complete zero-mode kernel is listed by chirality, charge, parity, and stratum; no mirror row survives; the manifest hash matches BND-A/B. | Only an index is reported, or the anomaly calculation uses a different field/domain manifest. | | SHP-C05 | Bundle/domain/anomaly certificate bundle | Spin or spin-c structure, bundle consistency, BRST domain, local anomalies, and global anomaly line all have passing certificates. | Any one of the domain, bundle, anomaly, or global-phase certificates is open. | | BND-C01 | Stratified-space inventory | Every regular stratum, fixed set, boundary, defect, corner, isotropy group, and normal representation is enumerated. | A fixed component or corner is absent from the manifest. | | BND-C02 | Cover/quotient conversion table | Volume factors, delta normalizations, parity traces, orientation signs, and gauge restrictions agree between the cover and quotient descriptions. | An unexplained factor of two or sign discrepancy remains. | | BND-C03 | Operator-domain certificate | Dirac, gauge, ghost, scalar, and load-bearing graviton domains are self-adjoint/elliptic as required and preserved by gauge/BRST transformations. | A parity table is supplied without a lawful operator domain. | | BND-C10 | Byte-identical shared manifest check | Chirality, family, spectrum, domain, and anomaly calculations consume the same frozen field/parity/domain hash. | The anomaly ledger silently uses different multiplicities or parities. | | BND-C11 | Boundary side-effect audit | The repair is checked for new edge modes, lost gauge symmetry, double counting, stress, vacuum terms, and changed heat-kernel coefficients. | A local anomaly repair creates an unowned physical effect. | | BND-C12 | Machine reconstruction + negative-control suite | A script rebuilds the fixed-set ledger and correctly classifies integrated-zero/local-nonzero, wrong-sign inflow, unquantized inflow, global-phase, domain, and gluing controls. | Any control is misclassified or a missing row defaults to zero. |

Package status and authority boundary

This file belongs to the Candidate-Neutral Building-Block Authority v3.3.2.

The package is documentation-complete for the current development architecture, but it is not protocol-frozen and not canonically ratified. Technical results generated under it remain development evidence until the control suite, enumeration test, and hostile review pass.

The controlling package authorities are:

EVIDENCEDISCHARGEREGISTRYV33_2.md;
QUANTITATIVESTOPPINGANDEXHAUSTIONRULEV33_2.md;
MANDATORYCONTROLSUITEV33_2.md;
MIGRATIONANDSUPERSESSIONRECORDV3_3.md.

A block is standalone for its owned object: it includes its complete definitions, interfaces, certificates, falsifiers, and owned evidence criteria. The full cross-block registry is intentionally stored once rather than repeated verbatim in every block.

Shared status grammar

PASS:
  The named witness satisfies the minimal discharge criterion.

FAIL:
  A reproducible counterexample or failed acceptance test exists.

OPEN:
  The required witness is missing, incomplete, or inconclusive.

NOT-EVALUATED:
  Evaluation stopped after an earlier hard failure.

NOT-APPLICABLE:
  A type proof establishes that the requirement cannot apply.

CONSTRUCTION-ANCHOR:
  A declared Actor, constraint, boundary term, or global sector realizes
  the result but does not derive it from the pre-existing object.

CONDITIONAL-ON-BND-A:
  The spectrum/domain result awaits fixed-set and operator-domain closure.

CONDITIONAL-ON-BND-B:
  The quantum result awaits local and global anomaly/inflow closure.

RESTART-REQUIRED:
  A frozen object relevant to the result changed.

Universal anti-promotion rules

A bare candidate is not a complete parent object.
A definition is not a witness.
A nonempty equation list is not a solvability proof.
An isolated vacuum is not automatically stable.
A fixed background value is not automatically an absent fluctuation.
Static vacuum-offset protection is not automatically cosmological-history compatibility.
Integrated anomaly cancellation is not local fixed-set cancellation.
Local anomaly cancellation is not global determinant-line trivialization.
A raw higher-dimensional quantity is not automatically the measured four-dimensional observable.
One tested survivor is not a selected survivor without explicit grammar enumeration or a finiteness theorem.

Appendix B — Exact BB-BND-B-1 source (verbatim)

--- title: "BB-BND-B-1 — Relative Anomaly, Quantized Inflow, Determinant Line, and Gluing" buildingblockid: "BB-BND-B-1" version: "1.0" date: "2026-07-24" status: "OPEN-RESEARCH CERTIFICATE AUTHORITY — METHOD COMPLETE, EXECUTION OWED" scope: "Split boundary authority under package v3.3.2" protocolfreeze: false canonicalratification: false packageauthorityversion: "3.3.2" ---

BB-BND-B-1 — Relative Anomaly, Quantized Inflow, Determinant Line, and Gluing

0. Status

OPEN-RESEARCH CERTIFICATE AUTHORITY.
FORMAL METHOD SPECIFIED.
CANDIDATE-SPECIFIC LOCAL/GLOBAL CALCULATION OWED.

This block carries the genuinely hard boundary problem. It is intentionally longer and has a different status from BND-A.

1. Preconditions

BND-A must pass. The global gauge group, charge lattice, tangential structure, field/domain manifest, orientations, and regulator convention must be frozen.

2. Local anomaly ledger

For each fixed set $F_a$,

\[ \mathcal Aa = \mathcal A{a,\rm projected\ bulk} + \mathcal A{a,\rm localized} + \mathcal A{a,\rm ghost/measure} + \mathcal A{a,\rm counterterm} + \mathcal A{a,\rm inflow}. \]

The complete vector must vanish:

\[ (\mathcal A1,\ldots,\mathcal AN)=0. \]

A zero integrated sum is not a pass.

3. Polynomial and convention completeness

For four-dimensional fixed sets, compute the full six-form anomaly polynomial and descent, including every applicable:

nonabelian cubic term;
mixed nonabelian–abelian term;
abelian cubic term;
mixed gravitational term;
local Lorentz/gravitational term;
projected bulk contribution;
localized field contribution;
ghost/measure contribution.

State whether the ledger uses consistent or covariant currents and record every Bardeen–Zumino shift.

4. Quantized inflow

An inflow term must identify:

parent Actor/action;
differential-form and trace normalization;
global group and charge lattice;
coefficient and quantization lattice;
large-gauge transformation;
boundary orientation signs;
local variation at each fixed set;
metric/vacuum response;
counterterm ambiguity;
pre-freeze provenance.

A fitted real coefficient is forbidden.

5. Global relative anomaly

After local cancellation, construct the determinant/anomaly line and prove a gluing-compatible trivialization using Dai–Freed, APS, relative bordism, invertible-field-theory, or an explicitly equivalent method.

For each declared mapping torus or bordism pairing, the total phase must be unity.

The global target must use the actual global gauge form and tangential structure.

6. BV/BFV quantum completion

Classical BRST nilpotency is insufficient. The boundary state, measure, ghosts, counterterms, and inflow must satisfy the relative quantum master equation and compose under gluing.

7. Gluing

For $Y=Y1\cupFY_2$,

\[ Z(Y)=\langle Z(Y1),Z(Y2)\rangle_F \]

must be independent of the arbitrary cut and compatible with orientation reversal.

8. Shared SG-3/UQF-4 identity

The chiral kernel and anomaly ledger must consume the same BND-A manifest. A no-mirror but anomalous theory fails both the unconditional chirality and quantum-consistency claims.

9. Heat-kernel and order-six interface

Localized heat-kernel coefficients may diagnose counterterms and anomalies, but they do not by themselves prove mode existence or determinant-line triviality. Any order-six boundary coefficient needed downstream must use the same domain and stratum manifest and carry its own witness.

10. Certificate

relative_anomaly_inflow_certificate:
  candidate_id:
  branch_id:
  bnd_a_manifest_hash:
  global_gauge_group:
  tangential_structure:
  anomaly_convention:
  regulator:
  fixed_set_anomaly_vector:
  counterterms:
  inflow_actions:
  quantization_tests:
  large_gauge_tests:
  determinant_line:
  eta_or_bordism_pairings:
  bv_bfv_completion:
  gluing_tests:
  heat_kernel_dependencies:
  vacuum_side_effects:
  evidence_hashes:
  verdict:

11. Mandatory controls

integrated-zero/local-nonzero;
wrong orientation sign;
unquantized fitted inflow;
local-zero/global-nontrivial;
wrong global gauge quotient;
arithmetic cancellation on an invalid domain;
gluing failure;
boundary repair creating an unowned light mode;
known positive relative-inflow model.

12. Closure terminal

CLOSED-SCOPED /
LOCAL FIXED-SET ANOMALY VECTOR ZERO /
QUANTIZED INFLOW PASS /
RELATIVE DETERMINANT-LINE TRIVIALIZATION PASS /
BV-BFV AND GLUING PASS /
SHARED CHIRALITY MANIFEST PASS.

Appendix — inherited complete v3.2 boundary/anomaly method

BB-BND-1.1 — Complete Standalone Orbifold Fixed-Set, Relative-Anomaly, and Inflow Completion

Authority and purpose

This block owns all boundary-, fixed-set-, defect-, interface-, and orbifold-local quantum-consistency obligations.

It exists because three statements are logically distinct:

\[ \text{bulk anomaly cancellation}, \qquad \text{local fixed-set cancellation}, \qquad \text{global relative anomaly trivialization}. \]

None implies the other two without a theorem.

The block is shared by:

UQF-4 global/quantum anomaly closure;
SG-3 chirality and no-mirror closure;
boundary spectra and heat-kernel calculations;
any BV/BRST claim on a quotient with fixed sets;
any vacuum or rigidity result using boundary terms.

1. Exact problem

Given a parent theory on a stratified space or quotient such as

\[ Y{d+1}=Md\times I, \qquad I=S^1/\mathbb Z2, \qquad \partial Y=F0\sqcup F_\pi, \]

determine whether:

the parity/domain assignment defines a lawful quantum operator;
each fixed set is locally gauge and gravitationally anomaly-free after all allowed inflow;
the complete partition function is a number rather than an untrivialized determinant-line element;
the construction composes correctly under cutting and gluing;
the same boundary data supports the claimed chiral spectrum.

2. Three ledgers

2.1 Domain ledger

For every field:

bulk representation;
global gauge representation;
parity at every fixed component;
surviving boundary value;
normal derivative condition;
self-adjoint extension;
ellipticity/strong ellipticity;
ghost and gauge-fixing boundary conditions;
zero-mode kernel.

2.2 Local anomaly ledger

For every fixed set $F_a$:

\[ \mathcal Aa = \mathcal A{a,\rm bulk-projected} + \mathcal A{a,\rm localized} + \mathcal A{a,\rm ghost/measure} + \mathcal A{a,\rm counterterm} + \mathcal A{a,\rm inflow}. \]

Require:

\[ \mathcal A_a=0 \]

for all gauge, mixed gauge–gravitational, and relevant local Lorentz anomalies.

2.3 Global relative ledger

The exponentiated eta invariant and fermion determinant define an element of a determinant/anomaly line.

The bulk invertible anomaly theory, boundary state, and counterterms must supply a gluing-compatible trivialization.

The pass condition is that every allowed closed test obtained by gluing, mapping torus, or bordism pairing has unit total phase.

3. Covering-space versus quotient-space rule

The candidate must choose a primary computation picture:

covering orbifold with equivariant traces and fixed-set distributions; or
quotient interval/manifold-with-boundary with boundary domains.

The second picture may verify the first, but conversion factors must be explicit.

Required conversion data:

quotient order;
fixed-point weights;
delta-function normalization;
bulk-volume normalization;
normal orientation;
parity trace;
gauge-transformation restriction.

An unexplained factor of $1/2$ is a failure.

4. Operator-domain completion

The boundary problem must be compatible with:

Dirac operator;
gauge kinetic operator;
ghost operator;
scalar/graviton operators where load-bearing;
BRST transformations;
gauge transformations preserving the domain.

A parity table alone is not an operator-domain certificate.

The certificate must show that the gauge/BRST transformation of an allowed field remains in the allowed domain.

5. Local anomaly polynomial

For a four-dimensional chiral fixed set, use a six-form anomaly polynomial

\[ I_6(F,R) \]

with descent

\[ I6=dI5^{(0)}, \qquad \delta I5^{(0)}=dI4^{(1)}. \]

The ledger must include all relevant coefficients, including:

$G^3$;
$G^2U(1)$;
$U(1)^3$;
$U(1)$-gravity;
local Lorentz/gravitational terms where applicable;
contributions of projected bulk fermions;
localized matter;
ghosts and measure terms when nontrivial.

The representation and trace normalization must use the actual global gauge group and charge lattice.

6. Locality of cancellation

The full integrated anomaly may vanish while gauge invariance fails at individual fixed sets.

Therefore the hard condition is:

\[ (\mathcal A0,\mathcal A\pi,\ldots)=0. \]

A nonzero vector with zero sum fails unless an allowed bulk current/inflow transports exactly the corresponding local anomaly with a globally well-defined action.

7. Inflow construction

An inflow term must identify:

parent field or topological Actor;
action and support;
coefficient;
quantization lattice;
large-gauge transformation behavior;
boundary orientation signs;
variation at every fixed set;
metric response;
counterterm ambiguity;
whether microscopic or matching-only.

The coefficient must be fixed before the fixed-set residual is read, or derived from a predeclared parent relation.

An arbitrary real coefficient is not closure.

8. Consistent/covariant-current firewall

Consistent and covariant anomalies differ by Bardeen–Zumino terms.

The ledger must not compare a consistent boundary anomaly with a covariant inflow current.

The convention and all Bardeen–Zumino shifts must be explicit.

9. Global anomaly and determinant line

A vanishing local polynomial is necessary but may not be sufficient.

For the declared tangential structure $\xi$ and global symmetry/gauge target $BG$, calculate the relevant relative anomaly theory using one or more of:

Dai–Freed eta-invariant construction;
Anderson-dual/cobordism classification;
APS index on a filling;
equivalent invertible-field-theory trivialization.

A closed-bulk bordism group alone is insufficient when the actual system has fixed-set boundary data. The certificate must show how the boundary condition determines or trivializes the anomaly line.

10. Gluing law

Let $Y=Y1\cupF Y_2$. The boundary states and eta/inflow phases must compose so that

\[ Z(Y) = \langle Z(Y1),Z(Y2)\rangle_F. \]

The result must be independent of the chosen cut and compatible with orientation reversal.

A boundary phase canceled separately on each piece but inconsistent under gluing fails.

11. Relation to chirality

The same parity/domain manifest must determine:

the zero-mode kernel;
the handedness split;
the fixed-set anomaly contributions.

Required consistency test:

\[ \text{kernel from domain} \longrightarrow \text{chiral spectrum} \longrightarrow \text{anomaly polynomial} \]

without changing conventions or field multiplicities.

A no-mirror spectrum that is anomalous is not a valid chirality solution.

12. Relation to BV/BRST

Classical Lie-algebra closure proves only classical nilpotency.

Quantum nilpotency requires the complete measure anomaly to vanish or be canceled:

\[ \frac12(S,S)-i\hbar\Delta S=0 \]

for the total boundary-completed system, or the appropriate BV–BFV relative equation before gluing.

The fixed-set/inflow ledger is therefore a necessary input to any order-$\hbar$ BRST claim.

13. Candidate-neutral closure constraints

| ID | Pass condition | |---|---| | BND-C01 | Complete stratum inventory | | BND-C02 | Consistent covering/quotient normalization | | BND-C03 | Lawful operator domain | | BND-C04 | Complete local anomaly polynomial at every stratum | | BND-C05 | Every local residual vanishes after allowed inflow | | BND-C06 | Inflow coefficients are predeclared and quantized | | BND-C07 | BV/BRST measure ledger passes | | BND-C08 | Correct global group and tangential structure | | BND-C09 | Determinant/anomaly line is trivialized | | BND-C10 | Chirality and anomaly use one manifest | | BND-C11 | No new unwanted modes, broken symmetries, or unowned vacuum terms | | BND-C12 | Machine reconstruction and negative controls pass |

14. Machine-readable certificate

boundary_anomaly_completion_certificate:
  candidate_id:
  branch_id:
  cover_and_quotient:
  global_gauge_group:
  tangential_structure:
  fixed_sets:
    - fixed_set_id:
      orientation_sign:
      restricted_gauge_group:
      allowed_gauge_transformations:
      localized_fields:
      parity_and_domain:
      projected_bulk_anomaly:
      localized_anomaly:
      ghost_measure_anomaly:
      counterterm_anomaly:
      inflow_anomaly:
      local_residual:
  anomaly_convention:
  trace_and_charge_normalization:
  inflow_actions:
  quantization_tests:
  bv_bfv_completion:
  determinant_line:
  eta_or_bordism_pairings:
  gluing_tests:
  chirality_manifest_hash:
  spectrum_manifest_hash:
  vacuum_dependency:
  negative_controls:
  evidence_hashes:
  verdict:

15. Required negative controls

Integrated-zero/local-nonzero: two fixed sets have opposite anomalies.
Parity-no-zero-mode: projected zero modes vanish but localized anomaly remains.
Wrong inflow sign: one boundary doubles rather than cancels.
Unquantized inflow: a fitted coefficient cancels locally but fails a large gauge transformation.
Local-zero/global-nontrivial: perturbative polynomials vanish but eta/bordism phase is nontrivial.
Domain failure: anomaly arithmetic passes but boundary conditions are not preserved by gauge/BRST transformations.
Gluing failure: separate pieces appear canceled but the composed phase is inconsistent.
Positive control: a known relative-boundary system with quantized inflow passes all stages.

16. UQF-4 full-closure terminal

UQF-4 FIXED-SET/INFLOW LEG:

LOCAL:
  Every fixed-set anomaly class vanishes after predeclared quantized inflow.

GLOBAL:
  The determinant/anomaly line is trivialized for the declared global
  gauge group and tangential structure, with gluing.

QUANTUM GAUGE:
  The boundary-completed BV/QME or equivalent quantum Ward identity passes.

SHARED CHIRALITY:
  SG-3 uses the identical parity/domain and field manifest.

TERMINAL:
  CLOSED-SCOPED / STRATIFIED-ANOMALY-CONSISTENT /
  RELATIVE-INFLOW-COMPLETE / RESOLVED +0.

This terminal is unavailable if only the closed-bulk bordism or integrated anomaly is known.

17. Explicit falsifiers and reopen triggers

This block is falsified or reopened by any of the following:

a nonzero local anomaly class at any fixed set;
a gauge transformation that does not preserve the declared boundary/operator domain;
a mismatch between the chirality field manifest and the anomaly field manifest;
an inflow coefficient outside its quantization lattice;
failure under a large gauge transformation;
a nontrivial determinant-line holonomy or eta/bordism pairing;
inconsistent orientation signs between covering and quotient descriptions;
a gluing law that depends on the arbitrary cut;
a boundary repair that introduces an undeclared light mode or breaks a required gauge symmetry;
a boundary/inflow change that was not propagated to the vacuum, spectrum, heat-kernel, rigidity, and chirality certificates;
a missing fixed component, localized sector, ghost/measure row, or allowed counterterm row;
any hard BND-Cxx cell reported as zero without a reproducible calculation or theorem.

A change to parity, fixed-set matter, global gauge form, tangential structure, regulator convention, or inflow action requires a new branch and a complete rerun.

18. Honest negative terminals

CLOSED-NEGATIVE /
LOCAL FIXED-SET ANOMALY SURVIVES.

OPEN /
GLOBAL DETERMINANT-LINE TRIVIALIZATION NOT COMPUTED.

RESTART-REQUIRED /
PARITY, GLOBAL GROUP, FIXED-SET CONTENT, OR INFLOW ACTION CHANGED.

19. Primary literature map

The block is aligned with the following primary references:

Dai and Freed, Eta-Invariants and Determinant Lines (1994), determinant-line and gluing formulation.
Scrucca, Serone, Silvestrini, and Zwirner, Anomalies in Orbifold Field Theories (2001), localized fixed-point anomalies despite integrated cancellation.
von Gersdorff, Quiros, and collaborators, Localized Anomalies in Orbifold Gauge Theories (2003), general fixed-set structure and cancellation.
Yonekura, Dai–Freed Theorem and Topological Phases of Matter (2016), physics formulation.
Davighi, Gripaios, and Lohitsiri, Global Anomalies in the Standard Model(s) and Beyond (2019), global gauge-group and bordism dependence.
Wan and Wang, cobordism classifications of Standard-Model and GUT anomaly structures.

These references supply methods and consistency checks. They do not replace the candidate-specific interval ledger.

Block-Specific Standalone Interface — Boundary, Orbifold, and Inflow

Owned questions

This block alone owns:

complete stratified boundary/fixed-set objects;
covering-to-quotient normalization;
boundary/operator domains;
localized perturbative anomalies;
consistent/covariant-current conventions;
quantized inflow and allowed counterterms;
determinant/anomaly lines;
relative bordism, eta phases, and gluing;
the shared chirality/anomaly manifest.

Required outputs

boundary anomaly completion certificate;
local anomaly vector for every fixed component;
inflow and quantization ledger;
BV/BFV or equivalent boundary completion;
determinant-line trivialization;
eta/bordism and gluing tests;
identity check with the chirality/spectrum manifest.

Non-ownership boundary

Boundary does not permit:

integrated cancellation to replace local cancellation;
zero local polynomial to replace global anomaly analysis;
parity arithmetic to replace a lawful operator domain;
a fitted real inflow coefficient;
unconditional chirality before the shared certificate passes.

Complete Reconstruction Procedure — Boundary, Fixed Sets, and Inflow

1. Interval reconstruction packet

For an interval obtained from $S^1/\mathbb Z_2$, reconstruct both descriptions:

Covering description

parent circle;
$\mathbb Z_2$ action;
fixed points;
equivariant field action;
parity traces;
fixed-point delta normalization.

Quotient description

interval;
two boundary components;
outward-normal orientation;
boundary conditions;
restricted gauge transformations;
localized field content.

The packet must show the exact map between them. No factor of $1/2$, orientation sign, or trace normalization may remain implicit.

2. Domain reconstruction

For every field and ghost, record:

bulk representation;
global representation;
parity at each fixed set;
allowed boundary value;
normal derivative condition;
self-adjoint extension;
ellipticity;
gauge/BRST preservation;
zero-mode kernel.

The same table must feed chirality, spectrum, anomaly, and heat-kernel calculations.

3. Local anomaly vector

For every fixed component $F_a$, calculate:

\[ \mathcal Aa = \mathcal A{a,\rm projected\ bulk} + \mathcal A{a,\rm localized} + \mathcal A{a,\rm ghost/measure} + \mathcal A{a,\rm counterterm} + \mathcal A{a,\rm inflow}. \]

The result is a vector

\[ \mathbf A{\rm fixed} = (\mathcal A1,\ldots,\mathcal A{NF}). \]

The pass condition is the zero vector. A zero sum with nonzero entries fails.

4. Inflow reconstruction

For every inflow term, record:

parent field;
action;
support;
differential-form and trace conventions;
coefficient;
quantization lattice;
large-gauge transformation;
orientation sign at every boundary;
local variation;
metric response;
counterterm ambiguity;
parent provenance.

The coefficient must not be fitted after reading the anomaly residual.

5. Global relative anomaly

After local cancellation, reconstruct:

determinant/anomaly line;
tangential structure;
global gauge target;
eta invariant or equivalent phase;
test bordisms or mapping tori;
topological inflow phase;
trivialization;
orientation reversal;
gluing law.

A vanishing perturbative polynomial is not a global certificate.

6. BV/BFV quantum completion

The reconstruction must show that:

allowed gauge transformations preserve the operator domain;
ghost boundary conditions are compatible;
measure anomalies are included;
the boundary state/functional completes the quantum master equation;
gluing two pieces gives the closed result.

Classical Lie-algebra closure alone is insufficient.

7. Shared chirality identity

The field list, parity table, representation multiplicities, and domain hash used to calculate the chiral kernel must be byte-identical to those used in the anomaly ledger.

A change in one requires both certificates to restart.

8. Side-effect audit

Every boundary repair must be checked for:

new massless edge modes;
broken required gauge symmetry;
double-counted localized fields;
changed boundary stress;
changed vacuum term;
changed heat-kernel coefficients;
changed rigidity or stability.

9. Final reconstruction test

A fresh agent must be able to reproduce these outcomes:

opposite wall anomalies with zero integrated sum fail;
wrong orientation inflow fails;
fitted unquantized inflow fails;
local cancellation with nontrivial eta phase fails;
non-BRST-preserving domain fails;
known positive relative-inflow example passes.

Only then is the boundary block executable and complete.

Owned hard constraints and acceptance evidence

The full controlling registry is EVIDENCEDISCHARGEREGISTRYV33_2.md. The rows below are embedded because this block owns or directly co-owns them.

| ID | Required witness | Minimal discharge | Fail trigger | |---|---|---|---| | BND-C04 | Fixed-set anomaly-polynomial ledger | At each fixed set, all projected bulk, localized, ghost/measure, mixed, and gravitational anomaly coefficients are calculated in one convention. | Only the integrated anomaly or one selected anomaly coefficient is shown. | | BND-C05 | Local residual vector calculation | The vector $(\mathcal A1,\dots,\mathcal AN)$ vanishes after allowed inflow at every component. | Nonzero wall anomalies cancel only after summing over the compact direction. | | BND-C06 | Quantized inflow/counterterm certificate | The parent inflow action, coefficient lattice, large-gauge test, orientations, and pre-freeze provenance are published. | A fitted real coefficient cancels the residual but is not globally quantized. | | BND-C07 | Boundary BV/BFV quantum-master-equation output | Ghost, measure, boundary state, and inflow contributions satisfy the relative QME and compose under gluing. | Classical BRST closure is used while the measure/domain anomaly remains. | | BND-C08 | Global-form/tangential-structure theorem input + exact target | The actual global gauge group, charge lattice, spin/pin/spin-c structure, and relative bordism target are fixed and justified. | Only the Lie algebra is used or the wrong bordism target is computed. | | BND-C09 | Dai–Freed/eta/bordism gluing certificate | The determinant line is trivialized and all declared mapping-torus/bordism pairings have unit total phase with cut-independent gluing. | Local polynomials vanish but a nontrivial global phase survives. | | BND-C10 | Byte-identical shared manifest check | Chirality, family, spectrum, domain, and anomaly calculations consume the same frozen field/parity/domain hash. | The anomaly ledger silently uses different multiplicities or parities. | | BND-C11 | Boundary side-effect audit | The repair is checked for new edge modes, lost gauge symmetry, double counting, stress, vacuum terms, and changed heat-kernel coefficients. | A local anomaly repair creates an unowned physical effect. | | BND-C12 | Machine reconstruction + negative-control suite | A script rebuilds the fixed-set ledger and correctly classifies integrated-zero/local-nonzero, wrong-sign inflow, unquantized inflow, global-phase, domain, and gluing controls. | Any control is misclassified or a missing row defaults to zero. |

Package status and authority boundary

This file belongs to the Candidate-Neutral Building-Block Authority v3.3.2.

The controlling package authorities are:

EVIDENCEDISCHARGEREGISTRYV33_2.md;
QUANTITATIVESTOPPINGANDEXHAUSTIONRULEV33_2.md;
MANDATORYCONTROLSUITEV33_2.md;
MIGRATIONANDSUPERSESSIONRECORDV3_3.md.

Shared status grammar

PASS:
  The named witness satisfies the minimal discharge criterion.

FAIL:
  A reproducible counterexample or failed acceptance test exists.

OPEN:
  The required witness is missing, incomplete, or inconclusive.

NOT-EVALUATED:
  Evaluation stopped after an earlier hard failure.

NOT-APPLICABLE:
  A type proof establishes that the requirement cannot apply.

CONSTRUCTION-ANCHOR:
  A declared Actor, constraint, boundary term, or global sector realizes
  the result but does not derive it from the pre-existing object.

CONDITIONAL-ON-BND-A:
  The spectrum/domain result awaits fixed-set and operator-domain closure.

CONDITIONAL-ON-BND-B:
  The quantum result awaits local and global anomaly/inflow closure.

RESTART-REQUIRED:
  A frozen object relevant to the result changed.

Universal anti-promotion rules

A bare candidate is not a complete parent object.
A definition is not a witness.
A nonempty equation list is not a solvability proof.
An isolated vacuum is not automatically stable.
A fixed background value is not automatically an absent fluctuation.
Static vacuum-offset protection is not automatically cosmological-history compatibility.
Integrated anomaly cancellation is not local fixed-set cancellation.
Local anomaly cancellation is not global determinant-line trivialization.
A raw higher-dimensional quantity is not automatically the measured four-dimensional observable.
One tested survivor is not a selected survivor without explicit grammar enumeration or a finiteness theorem.

Appendix C — Exact BB-AD-1 source (verbatim)

BB-AD-1 — Anomaly-Descent Chiral-Domain and Mirror-Completeness Building Block

Version: 1.0 Date: 2026-07-17 Owner: Shape / Rulebook / Dynamics Status: Controlling UQF-7 building block under Shape v2.10.

1. Pair

\[ \boxed{ \Xi{\rm AD}^{\rm pair} = \Xi{\rm CDO}\dashv\Xi_{\rm MSC}^{\vee} } \]

$\Xi_{\rm CDO}$: Chiral-Domain and Orbifold-Parity Actor.
$\Xi_{\rm MSC}^\vee$: Mirror-Source, Spectrum, and Regulator-Completeness Co-Actor.

Neither object adds a metric dimension, particle species, measured Scale anchor, or continuous fitting parameter.

2. Actor tuple

\[ \Xi{\rm CDO}= (I\chi,\mathscr R\chi,\Pi{\rm adm},D{13}, \mathcal H{\le M*},\{hm}\,,\mathcal R_{4D}). \]

The Actor owns the folded interval, the species-by-species parity table, the self-adjoint Dirac domain, the pre-quantization Scale projector, the admitted finite operational Hilbert space, the exact intertwining of every microscopic move with the parity projector, and the four-dimensional chiral readout.

3. Co-Actor domain

\[ \operatorname{Mir}{\rm lawful} = \{M0,M1,M2,M3,M4,M5,M6,M7,M8,M9,M{10}\}, \]

with the categories recorded in mirrorcategorytruth_table.csv: zero modes, KK modes, fixed-set modes, regulator doublers, auxiliary mirrors, composites, elementary-overlap poles, parity-breaking moves, global anomalies, inflow mismatches, and future Actor additions.

4. Exact certificates

\[ \operatorname{ind}D{\rm adm}=3, \qquad \ker D{\rm mirror}^{(0)}=0. \]

\[ [hm,\Pi{\rm adm}]=0 \quad\forall m\in\mathfrak M_{\rm legal}. \]

Using the frozen Shape relation $R\chi=R6/2$,

\[ \lambda{\min}(D{\rm mirror}^\dagger D{\rm mirror}) =\frac1{R\chi^2}, \qquad m{\rm mirror,1}=\frac1{R\chi}=4\pi M_U. \]

Numerically,

\[ m{\rm mirror,1}=1.256637061435917e+17\;{\rm GeV} =1.580135694410067\,M*, \]

so every mirror-capable nonzero interval mode lies outside the admitted operational spectrum.

For every gauge-breaking mirror bilinear $B_{\rm break}$,

\[ \Pi{\rm phys}B{\rm break}\Pi_{\rm phys}=0. \]

The mirror block has no zero-energy kernel and contributes no topological ground-state degeneracy.

4A. Scale synchronization

The spectral and volume ledgers use one quotient convention:

\[ R\chi=R6/2, \quad \mathrm{Vol}(I\chi)=\pi R\chi=1/(4MU), \quad M*=7.9527161235673120e+16\;\mathrm{GeV}. \]

Hence

\[ m{\rm mirror,1}/M*=1.580135694410067>1. \]

A radius, volume, or cutoff change is a versioned reopen trigger.

4B. Operational source-domain theorem

Define

\[ \mathcal H{\rm phys}=Q{\le M*}\Pi{\rm adm}\mathcal H_{\rm parent}. \]

The wrong-parity zero-mode kernel is empty and every nonzero opposite-parity parent level begins above $M_*$. Therefore

\[ \boxed{Q{\rm opp}\mathcal H{\rm phys}=0.} \]

The KK threshold certifies the source inventory used to build the finite theory. It is not a nonrenormalization theorem for a heavy pole retained by some future regulator. A future branch that includes such a state must prove its interacting gap and decoupling separately.

5. SMG disposition

The historical SMG Actor is removed from the controlling branch because the current relational regulator does not introduce an auxiliary mirror Hilbert sector. SMG remains a valid alternative architecture for a future regulator that does introduce mirrors. Such a future branch must independently prove a positive gap, vanishing gauge-breaking bilinears, and absence of topological degeneracy; it cannot inherit the present closure automatically.

6. Scope

The theorem protects the fundamental chiral source algebra and proves that the accepted finite microscopic basis contains no opposite-parity elementary state. It does not claim that no massive anomaly-trivial vectorlike composite can ever exist. Such composites do not alter the family index or anomaly descent and are not counted as additional fundamental families.

7. Reopen conditions

The gate reopens on any change to the interval radius, parity table, fixed-set domain, fermion Actor inventory, local move grammar, anomaly category, operational cutoff, or observer definition of an elementary mirror pole.

BB_DYN_4_2_MAX_RIGOR_FULL_GATE_CLOSURE_DYNAMICS.md1,55,401 bytes

scale/06_SOURCES/BB_DYN_4_2_MAX_RIGOR_FULL_GATE_CLOSURE_DYNAMICS.md

--- title: "BB-DYN-4.2 — Maximum-Rigor Full Gate-Closure Dynamics Object" buildingblockid: "BB-DYN-4.2" version: "4.2" date: "2026-08-02" status: "DEVELOPMENT AUTHORITY CANDIDATE — MAXIMUM-RIGOR PRESERVATION-AUDITED STANDALONE GATE-EXECUTION OBJECT — NOT FROZEN" supersedesfordevelopment: "BB-DYN-4.1" preserves: "All substantive BB-DYN-3.3.1 obligations, DYN-C01 through DYN-C08, boundary/orbifold authority, standalone interface, certificates, controls, status grammar, and anti-promotion rules" claim_ceiling: "Defines required Dynamics objects, algorithms, evidence, controls, preservation obligations, and terminals; does not assert that gate-specific calculations pass." ---

BB-DYN-4.2 — Maximum-Rigor Full Gate-Closure Dynamics Object

0. Executive verdict

Dynamics is the complete lawful-change object acting on the frozen Shape. It is not merely an action, an equation list, a Hessian, or a beta function. A gate receives Dynamics support only when the relevant chain is executed:

\[ \text{Shape inputs} \rightarrow\text{parent law} \rightarrow\text{constraint/measure reduction} \rightarrow\text{background} \rightarrow\text{physical operators} \rightarrow\text{interactions and transitions} \rightarrow\text{quantum/history/causal evolution} \rightarrow\text{refinement and regional balance} \rightarrow\text{finite Observer records}. \]

This file is standalone for the Dynamics object. It contains the owned physical questions, the complete seventeen-row constraint system, thought-experiment derivation, cross-block contracts, generation and saturation algorithms, packet schemas, all-gate profiles, destructive controls, residual vector, evidence tree, validator logic, and terminal rules. Definitions are not witnesses; gate-specific calculations must still be executed.

1. Why V4.0 was not complete

V4.0 correctly identified nine missing reusable obligations, but it remained an expanded specification. Several new rows were short prose requirements; packet schemas were incomplete or stored separately; the Stage–Rulebook–Actor compiler was not explicit; interaction and operator saturation were not algorithmic; all-gate profiles were outside the authority; and no standalone validator or residual theorem connected evidence to a terminal. V4.1 repaired those operational gaps without claiming new gate results. V4.2 additionally performs a full preservation audit against BB-DYN-3.3.1 and restores every legacy normative clause that V4.1 did not explicitly carry into its main execution text.

2. Dynamics identity, ownership, and non-ownership

2.1 Owned object

Dynamics owns the parent law and every lawful transformation from admitted configurations to physical evolution and response. Its owned object is

\[ \mathfrak D=(S{\mathrm{parent}},\mathcal F,\mathcal C,\mu{\mathrm{phys}},\bar z,\mathfrak O_{\mathrm{phys}},\mathfrak I,\mathfrak T,\mathfrak Q,\mathfrak H,\mathfrak R,\mathfrak J), \]

where the entries are respectively the parent law, equation vector, constraint system, physical measure, lawful background, physical operator shelf, interaction hypergraph, transition/mass system, quantum physicality and channels, nonequilibrium/causal histories, refinement system, and regional currents/fluxes.

2.2 Non-ownership firewall

Shape owns supports, admissibility, and Actor identities; Dynamics cannot invent a support, rule, or Actor to make a gate pass.
Granularity owns operational equivalence, candidate/mode exhaustion, and stopping; Dynamics supplies the calculated objects it audits.
Scale owns rulers, numerical provenance, matching conventions, and uncertainty transport.
Boundary A/B owns exact domains, fixed-set kernels, local/global anomaly and inflow closure, although Dynamics consumes and tests them.
Rigidity owns deformation/stability terminals; Dynamics supplies the physical Hessian and evolution.
Vacuum owns constant-shift protection; Dynamics supplies full equations, stress, and finite-time response.
Observer owns record maps and calibration; Dynamics supplies lawful response and channels.
Time Synchronization owns clock compatibility; Dynamics supplies characteristic support and evolution.
Interdependence/governance owns branch hashes, stale propagation, evidence status, and terminal issuance.

3. Completeness theorem for the Dynamics object

For the frozen branch, a Dynamics responsibility is in scope if changing it while holding Shape and the other block inputs fixed can change at least one lawful physical trajectory, amplitude, spectrum, probability, history, or finite record. Such changes fall into exactly the following current families:

parent-law ownership;

constraint/gauge closure;

physical measure;

stress and source response;

background/reaction solvability;

quantum/domain/anomaly consistency;

ordinary causal response;

scope and tails;

physical operators and spectra;

interactions and sources;

masses/mixings/transitions;

quantum positivity and continuation;

closed/open probability evolution;

nonequilibrium and thermal history;

well-posed causal evolution;

RG/refinement stability;

regional/interface flux balance;

These families are represented by DYN-C01 through DYN-C17. Completeness is current-branch and grammar-relative, not metaphysical. The block reopens if a gate produces a lawful dynamics distinction not representable by these families.

Define the Dynamics closure operator Cl_DYN as repeated application of term generation, equation variation, constraint closure, physical reduction, interaction generation, history/refinement generation, and complement testing. The object is saturated at a gate only when a new pass produces no new in-grammar term, equation, constraint, physical operator, interaction edge, transition, channel, history variable, refinement direction, or regional current.

4. Frozen input contracts

4.1 Stage input

branch/support IDs; metric, topology, strata, incidence, volume, curvature, orientation, variational and deformation ledgers; cover/quotient normalization.

4.2 Rulebook input

representations, parities, domains, quotients, exact constraints, global form, positivity requirements, interaction permissions, regulator rules, claim ceilings.

4.3 Actor input

owner IDs, supports, representations, equations, split/merge criteria, modes versus identities, kill and reopen conditions.

4.4 Co-Actor input

all applicable parent, owner, domain, quotient, measure, spectrum, interaction, rigidity, regulator, and exhaustion attack classes.

4.5 Granularity input

candidate/mode grammar, cutoff, equivalence relation, tail obligations, omitted-rival and stopping rules.

4.6 Scale input

rulers, units, radii, gaps, renormalization/matching scheme, uncertainties, transport maps.

4.7 Boundary input

self-adjoint/elliptic domains, parity and fixed-set data, gluing, edge kernels, anomaly/inflow and relative-QME certificates.

4.8 Observer input

record space, projection, normalization, calibration, accessibility and no-signalling criteria.

4.9 Rigidity/Vacuum/TS input

deformation basis and terminal criteria; constant-shift tests and history scope; clock and causal-composition rules.

4.10 Governance input

authority hashes, gate contract, frozen assumptions, evidence registry, status grammar, reopen propagation.

Every input is hash-bound. A missing or stale input yields OPEN or RESTART-REQUIRED, never an inferred default.

5. Shape-to-Dynamics compilation contract

The compiler consumes the frozen three-layer Shape and returns physical Dynamics packets without reading the desired gate answer.

\[ \mathsf{Compile}_{\mathrm{DYN}}=\mathsf{Refine}\circ\mathsf{Evolve}\circ\mathsf{Quantize}\circ\mathsf{Transition}\circ\mathsf{Interact}\circ\mathsf{Reduce}\circ\mathsf{Vary}\circ\mathsf{Generate}. \]

5.1 Pass A — Generate

Generate every admissible parent term and primitive move from Stage supports, Rulebook permissions, Actor owners, tensor/representation grammar, derivative scope, strata, and global classes. No target-dependent term may be inserted.

5.2 Pass B — Vary

Vary every retained variable and boundary/global datum, or publish an explicit lawful equation disposition. Produce the complete bulk–boundary–global equation vector.

5.3 Pass C — Reduce

Run constraint/gauge/BV/BFV closure, construct the physical measure, solve or classify the background, and build the physical quotient.

5.4 Pass D — Interact and transition

Generate the complete interaction/source hypergraph, then derive masses, mixings, transitions, decays, and thresholds only from owned edges and solved backgrounds.

5.5 Pass E — Quantize and evolve

Construct positive physical sectors, closed/open channels, causal initial-boundary evolution, nonequilibrium histories, and regional flux balances.

5.6 Pass F — Refine and saturate

Run nested-basis, regulator, tower, history-resolution, and omitted-tail controls. Pass outputs to Granularity for equivalence and exhaustion.

6. Universal object and packet grammar

Every Dynamics object uses the following base record:

dynamics_object:
  object_id:
  branch_id:
  gate_id:
  owner_actor_ids: []
  stage_support_ids: []
  rulebook_rule_ids: []
  boundary_domain_ids: []
  scale_packet_id:
  granularity_scope_id:
  parent_object_ids: []
  assumptions: []
  equations_or_maps: []
  evidence_files: []
  evidence_hashes: []
  calculation_order:
  scope_ceiling:
  destructive_controls: []
  unresolved_residuals: []
  status: PASS|FAIL|OPEN|NOT-EVALUATED|NOT-APPLICABLE|RESTART-REQUIRED

No packet may use an Actor name, expected multiplicity, observed matrix, or desired terminal as its derivation. Such data may appear only as a later comparison target.

6A. Preserved full mathematical kernel from BB-DYN-3.3.1

The following kernel is retained normatively rather than summarized. It supplies the detailed parent-action, equation, constraint, measure, stress, reaction, background, radiative, stability, vacuum-response, probability, causality, conservation, and boundary/orbifold formulas that V4.0 did not fully integrate into its standalone file. V4.1 additions refine execution and evidence; they do not erase these equations.

1. Parent action

Every candidate must supply a typed parent action or an explicitly scoped non-action replacement.

A general action ledger is

\[ S{\mathrm{parent}}=S{\mathrm{grav}}+S{\mathrm{gauge}}+S{\mathrm{matter}}+S{\mathrm{scalar}} +S{\mathrm{boundary}}+S{\mathrm{constraint}}+S{\mathrm{global}}+S_{\mathrm{domain}}. \]

For every term publish:

support and dimensionality;
field owner;
derivative order;
exact and broken symmetries;
coefficient provenance;
boundary variation;
whether microscopic, structural, global, or matching-only;
stress-energy contribution;
vacuum-energy contribution;
cutoff and scheme scope.

An arbitrary dense kernel entry without a parent-law owner is prohibited.

2. Complete equation vector

Let the independent variables be

\[ z^I=(g{\mu\nu},\gamma{mn},g{\mu m},AM,\Psi,\phi,b,\lambda,\sigma,\ldots). \]

The complete background and fluctuation equations are

\[ \mathcal F_I[z]\equiv\frac{\delta\Gamma}{\delta z^I}=0, \]

supplemented by boundary, global, gauge, and constraint equations.

The candidate must publish an equation ledger:

equation:
  equation_id:
  varied_object:
  local_or_global:
  bulk_or_boundary:
  differential_or_algebraic:
  independent_after_identities:
  source_terms:
  constraint_couplings:
  observer_projection:
  solution_status:

2.1 Equation counting

Before claiming a background solution:

count independent unknown functions and global variables;
count independent equations after Noether and Bianchi identities;
classify gauge freedoms;
classify second-class constraints;
include boundary and junction equations;
verify rank on the claimed stratum;
prove or compute existence of a solution.

A visually plausible product ansatz is not a solution certificate.

3. Constraint classification and closure

Constraints are typed as:

first-class gauge constraints;
second-class physical constraints;
constitutive restrictions;
boundary/gluing constraints;
global constraints;
effective matching relations.

For Hamiltonian variables, the total Hamiltonian is

\[ HT=H0+u^A\Xi_A. \]

The Dirac–Bergmann algorithm must:

list primary constraints;
impose preservation $\dot\Xi_A\approx0$;
generate every secondary and higher constraint;
terminate with constant rank on the claimed stratum;
classify first- and second-class sectors;
determine multipliers and residual gauge functions;
verify boundary compatibility;
compute the physical degree-of-freedom count.

For second-class constraints,

\[ C{AB}=\{\XiA,\Xi_B\} \]

must be invertible on the physical stratum and

\[ \{F,G\}D=\{F,G\}-\{F,\XiA\}(C^{-1})^{AB}\{\Xi_B,G\}. \]

Rank change is a branch change or singular stratum, not a small correction.

4. Physical measure

For a second-class system,

\[ D\mu{\mathrm{phys}}=D\mu0\prodA\delta(\XiA)\sqrt{\det C}. \]

The determinant must be included in effective actions, matching, and stress calculations.

If $C$ depends on retained fields,

\[ \Delta\Gamma_C=-\frac{i}{2}\operatorname{Tr}\log C \]

or the appropriate Euclidean counterpart contributes physical terms.

A field-dependent determinant cannot be dismissed as normalization.

5. No-work and stress are separate

For ideal constraints,

\[ \lambda^A d\Phi_A=0 \]

along admissible displacements.

This proves no virtual work in constrained directions. It does not establish zero stress-energy.

For

\[ S{\rm constraint}=\int d^Dx\sqrt{-g}\,\lambda^A\PhiA, \]

\[ T^{\rm constraint}{MN} =-\frac{2}{\sqrt{-g}}\frac{\delta S{\rm constraint}}{\delta g^{MN}}. \]

The calculation must include:

metric variation of the volume form;
explicit metric dependence of $\Phi_A$;
metric dependence of multipliers when induced by solved equations;
determinant and ghost terms;
boundary contributions.

Zero constraint stress is a result with conditions, not a default property.

6. Constrained reaction equations

For retained variables $q^a$, constrained variables $\phi^r$, and constraints $\Phi_\alpha(q,\phi)=0$, the renormalized equations are

\[ \frac{\delta\Gamma0}{\delta q^a} +\lambda^\alpha\frac{\delta\Phi\alpha}{\delta q^a}=0, \]

\[ \frac{\delta\Gamma0}{\delta\phi^r} +\lambda^\alpha\frac{\delta\Phi\alpha}{\delta\phi^r}=0, \]

\[ \Phi_\alpha=0. \]

6.1 Block-separable case

\[ \frac{\delta\Phi_\alpha}{\delta q^a}=0 \]

and the normal Jacobian

\[ N{\alpha r}=\frac{\delta\Phi\alpha}{\delta\phi^r} \]

has full rank, the normal equations determine reactions when

\[ -\left.\frac{\delta\Gamma0}{\delta\phi^r}\right|{\Phi=0} \in\operatorname{im}N^T. \]

This prevents normal-force overdetermination only under that span condition.

6.2 General case

If constraints depend on retained variables, multipliers modify retained equations. The full coupled system must be solved.

6.3 Global solvability

Pointwise algebra is insufficient. The multiplier system must satisfy:

regularity;
boundary and fixed-set parity;
junction conditions;
global integrability;
Ward identities;
anomaly cancellation;
conserved-charge balance.

7. Background-equation completeness

A candidate background receives one of four Dynamics statuses:

7.1 Parent solution

Every varied parent equation and boundary equation is satisfied.

7.2 Constrained reaction solution

Displaced equations are replaced by a complete, solvable reaction system, including stress and boundary effects.

7.3 Effective external background

The Stage is externally supplied. The reduced theory may be useful, but it does not derive the background as a parent vacuum.

7.4 Inconsistent background

The complete equation system has no solution at the claimed object.

A closure statement must name which status is used.

8. Radiative solvability

Let $\Gamma_k$ be the effective action at scale $k$. Radiative consistency requires more than preservation of the classical constraint surface.

At each claimed order or Wilsonian step, test:

closure of the corrected constraint algebra;
rank stability;
normal-force span;
retained equation solvability;
boundary compatibility;
anomaly and Ward identities;
generation of forbidden operators;
determinant contributions;
parameter and counterterm provenance.

A forbidden mode need not be regenerated for the theory to fail. Equations with no solution are a separate failure.

9. Physical stability interface

Dynamics supplies the effective Hessian to BB-RIG-1.1.

After gauge quotient and exact constraints,

\[ Q{\rm phys}=P{\rm phys}^{T}\,\delta^2\Gamma\,P_{\rm phys}. \]

The supplied packet must include:

kinetic metric;
gauge fixing and ghosts;
mixed blocks;
boundary domain;
scale and scheme;
zero modes;
negative modes;
intended protected scalars;
tower scope;
uncertainty.

Dynamics may not label an isolated critical point stable without the physical Hessian result.

10. Vacuum-offset response interface

A field-independent shift of a protected matter sector is

\[ \mathcal Lm\rightarrow\mathcal Lm-c. \]

Dynamics must expose how it enters the complete equations.

For ordinary Einstein coupling, the external equation shifts by a term proportional to

\[ c\,g_{\mu\nu}. \]

Constraint reactions in internal directions do not automatically remove this external response.

The vacuum-response packet sent to BB-VAC-1.1 contains:

vacuum_response_packet:
  protected_sector:
  constant_shift_parameter:
  external_metric_equation:
  internal_equations:
  constraint_reaction_equations:
  global_auxiliary_equations:
  boundary_equations:
  determinant_terms:
  matching_terms:
  graviton_loop_scope:
  ordinary_stress_response:
  solved_response_operator:

11. Ordinary-gravity control

Any vacuum-offset mechanism must preserve lawful response to nonconstant stress.

The negative control is:

add a constant $-c$ to the protected Lagrangian;
verify local curvature observables do not change in the protected scope;
add a localized excitation with nontrivial traceless or gradient stress;
verify ordinary gravitational response remains.

A mechanism that removes all stress from the gravitational equations fails.

12. Constant shifts versus phase transitions

A constant threshold correction and a finite-time phase transition are distinct.

Dynamics must classify:

static additive shift;
changing condensate;
latent heat;
radiation production;
nonadiabatic boundary or global response;
historical averages;
residual present value.

A constant-shift identity does not automatically solve cosmological transition history.

13. Probability, causality, and conservation

For closed quantum sectors, the generator must be self-adjoint on the physical domain or possess an equivalent unitary kernel.

For open sectors, declare:

environment;
channel;
normalization;
exchange currents;
observer access;
approximation bound.

The law must preserve, at the claimed scope:

probability;
gauge and BRST constraints;
exact charges;
boundary flux balance;
causal support;
operational no-signalling.

Integrated boundary/orbifold authority

This block is part of the Candidate-Neutral Building-Block Authority v3.1 — Boundary and Inflow Development Candidate.

The following rule is binding across the set:

A bulk or quotient-space anomaly cancellation statement does not close a theory with orbifold fixed sets or physical boundaries. Each stratum requires a local anomaly ledger, and the complete quantum theory requires a relative/global trivialization compatible with gluing.

The dedicated owner is BB-BND-1 — Orbifold Fixed-Set, Relative-Anomaly, and Inflow Completion.

Every candidate containing a boundary, fixed set, defect, quotient singularity, interface, or parity projection must provide a boundaryanomalycompletion_certificate. Until that certificate passes:

a chirality or no-mirror result is CONDITIONAL-ON-BND;
quantum BRST/BV nilpotency is CONDITIONAL-ON-BND;
a global-bordism result for the closed bulk target is not a complete boundary result;
cancellation after integrating over the compact direction is not accepted as local gauge invariance;
no gate may claim that the interval/orbifold construction is fully quantum consistent.

Boundary/orbifold completion — stratified quantum gauge consistency

1. Complete gauge variation

For a $d+1$-dimensional parent with $d$-dimensional fixed sets $F_a$, the renormalized gauge variation is decomposed as

\[ \delta\epsilon\Gamma{\rm tot} = \delta\epsilon\Gamma{\rm bulk} + \suma \delta\epsilon\Gamma{Fa} + \delta\epsilon S{\rm inflow} + \delta\epsilon S{\rm ct}. \]

For four-dimensional fixed sets, write the descent data

\[ I6=dI5^{(0)}, \qquad \delta\epsilon I5^{(0)}=dI_4^{(1)}(\epsilon,A). \]

A bulk inflow action of the form

\[ S{\rm inflow} = 2\pi i\,k\int{Y5}I5^{(0)} \]

has boundary variation

\[ \delta\epsilon S{\rm inflow} = 2\pi i\,k \suma sa \int{Fa}I_4^{(1)}, \]

where $s_a$ is fixed by the outward-normal orientation. The coefficient $k$ must satisfy the appropriate quantization and global-form conditions.

2. Fixed-set local equations

For each fixed set define

\[ \mathcal Aa^{(1)} = \mathcal A{a,\rm projected\ bulk}^{(1)} + \mathcal A{a,\rm localized}^{(1)} + \mathcal A{a,\rm measure}^{(1)} + \mathcal A{a,\rm counterterm}^{(1)} + \mathcal A{a,\rm inflow}^{(1)}. \]

The local pass condition is

\[ \boxed{\mathcal A_a^{(1)}=0\quad\text{for every }a} \]

as a cohomology class under all allowed gauge transformations.

The weaker condition

\[ \suma\mathcal Aa^{(1)}=0 \]

is only an integrated check. It does not prove local gauge invariance.

3. Quantum master equation with boundaries

The candidate must formulate the quantum gauge system using BV–BFV or an equivalent boundary-complete formalism.

Schematically,

\[ \frac12(S,S)-i\hbar\Delta S = \pi^*S_{\partial} \]

before boundary completion. Full closure requires a compatible boundary state/functional and counterterm/inflow system such that the total quantum master equation is satisfied.

A bulk statement $Q_{\rm BRST}^2=0$ is insufficient when the measure has fixed-set support.

4. Consistent versus covariant anomalies

The ledger must state whether it uses:

consistent anomalies;
covariant anomalies;
Bardeen–Zumino shifted currents.

All fixed-set and inflow entries must use one compatible convention. A Bardeen–Zumino polynomial may redistribute anomaly between currents or strata, but it cannot remove the total anomaly class.

5. Regulator and parity dependence

Localized anomalies can depend on the parity/domain assignment and on how bulk fermions are regulated. The final anomaly class must be regulator-independent after allowed local counterterms are included.

The certificate must report:

regulator;
consistent-current convention;
parity signs;
fixed-set weights;
localized spectrum;
allowed counterterms;
invariant remainder.

6. Global relative anomaly equation

Perturbative cancellation is not enough. The exponentiated fermion determinant is a section of an anomaly/determinant line.

The complete parent-plus-boundary system must provide a gluing-compatible trivialization:

\[ Z{\rm boundary}\, Z{\rm inflow} \in\mathbb C \]

rather than an untrivialized line.

For every closed test obtained by gluing or forming a mapping torus, require

\[ \exp\!\left(2\pi i\,\frac{\eta+h}{2}\right) \, \exp(2\pi i S_{\rm top}) = 1 \]

in the declared convention and tangential structure.

7. Dynamics certificate additions

boundary_quantum_dynamics:
  fixed_set_ids:
  allowed_gauge_transformations:
  anomaly_convention: consistent|covariant
  regulator:
  bulk_anomaly_polynomial:
  projected_bulk_contributions_by_fixed_set:
  localized_field_contributions:
  measure_and_ghost_contributions:
  counterterms:
  inflow_action:
  inflow_coefficient_quantization:
  orientation_signs:
  local_residuals:
  bv_bfv_or_equivalent_completion:
  determinant_line:
  relative_eta_or_bordism_test:
  gluing_test:
  quantum_master_equation_result:
  evidence_hashes:
  verdict:

8. New Dynamics falsifiers

Dynamics fails if:

only the integrated anomaly is zero;
an inflow coefficient is selected after reading the residual;
the coefficient is not globally quantized;
a boundary condition is not compatible with the Dirac/gauge operator domain;
the local anomaly convention changes between rows;
the determinant line remains untrivialized;
the BV quantum master equation is asserted from classical Jacobi closure alone.

6B. Normative preservation layer from BB-DYN-3.3.1

This section restores every substantive legacy obligation that was not explicit in the V4.1 execution text. It is additive and binding. V4.2 may strengthen a legacy requirement, but may not silently weaken or delete it. Where a V4.2 clause and a legacy clause overlap, the stricter evidentiary requirement controls unless a gate-scoped supersession record identifies the exact clause, reason, replacement witness, and claim-ceiling effect.

6B.1 Original physical question and four anti-substitution firewalls

Dynamics answers:

Which lawful changes occur on the complete Shape, which equations define its backgrounds, how exact constraints are preserved, how quantum corrections modify the equations, and how the system responds separately to vacuum offsets and ordinary excitations?

This block prohibits four substitutions:

\[ \text{kinematic permission}\neq\text{nonzero amplitude}, \]

\[ \text{constraint no-work}\neq\text{zero stress}, \]

\[ \text{no propagator}\neq\text{radiative solvability}, \]

\[ \text{internal reaction solvable}\neq\text{vacuum energy degravitated}. \]

6B.2 Legacy Dynamics certificate remains a mandatory compatibility view

The V4.2 integrated certificate must be able to emit every field of the original dynamicscertificatev3. A missing legacy field is not excused merely because a newer packet contains related information.

dynamics_certificate_v3:
  candidate_id:
  branch_id:
  parent_action:
  primitive_term_ledger:
  complete_equation_vector:
  equation_count_and_identities:
  constraint_types:
  dirac_bergmann_closure:
  rank_strata:
  physical_measure:
  determinant_contributions:
  constraint_stress:
  multiplier_boundary_problem:
  background_status:
  background_solution:
  radiative_solvability:
  ward_identities:
  anomaly_result:
  physical_hessian_packet:
  vacuum_response_packet:
  ordinary_gravity_control:
  phase_transition_scope:
  full_tower_scope:
  evidence_hashes:
  verdict:

6B.3 Legacy destructive controls

The following four controls remain mandatory whenever their types apply. They supplement, rather than replace, the V4.2 thought-experiment suite.

15.1 No propagator but no solution

Remove a deformation field from the propagator but choose a radiative normal force outside the multiplier span.

Expected result: FAIL / RADIATIVE OVERDETERMINATION.

15.2 Constraint no-work with nonzero stress

Use a metric-dependent constraint that does no virtual work along admissible motion.

Expected result: no-work passes, stress-zero claim fails.

15.3 Vacuum degravitation that also removes matter gravity

Project out every trace and traceless source indiscriminately.

Expected result: vacuum shift passes, ordinary-gravity control fails.

15.4 Frozen Stage with abandoned internal equations

Do not vary the internal metric and supply no reaction or background equation.

Expected result: EFFECTIVE EXTERNAL BACKGROUND, not parent solution.

6B.4 Legacy falsifiers and reopen triggers

This block fails or reopens if:

the parent action is incomplete;
a primitive move lacks an owner;
equation counting omits a boundary or global equation;
Dirac closure or rank is incomplete;
determinant terms are omitted;
no-work is used as a stress proof;
no-propagator is used as a solvability proof;
a background is called a solution without all equations;
a constant vacuum shift changes local curvature in the claimed protected scope;
ordinary nonconstant stress fails to gravitate;
a phase-transition claim is inferred from constant-shift cancellation;
a zero-mode result is promoted to the full tower.

6B.5 Legacy terminal and delivery scope

The following is retained as the historical minimum delivery claim of the Dynamics block. The current authority identifier and status are controlled by V4.2 frontmatter and Section 19.

BB-DYN-3.3.1

DELIVERS:
  Parent law, complete equations, constraint and measure closure,
  background solvability, stress accounting, radiative response,
  and interfaces to rigidity and vacuum protection.

STATUS:
  DEVELOPMENT AUTHORITY CANDIDATE — NOT FROZEN.

6B.6 Complete standalone ownership interface

The full prior standalone interface is retained below. References to package v3.3.2 remain provenance statements; current evidence generation must additionally satisfy the V4.2 registries and validators.

Owned questions

This block alone owns:

the typed parent action;
the complete equation vector;
constraint classification and preservation;
physical measure and determinant ownership;
stress of multiplier, boundary, and constraint sectors;
retained/reaction-equation solvability;
Ward identities and BV/BFV quantum consistency;
ordinary probability, causality, conservation, and nonconstant-stress response.

Required inputs

complete Shape and boundary manifests;
constraint and permission packets;
Scale/scheme packet;
complete field and Actor inventory;
candidate-specific parent terms.

Required outputs

parent-action manifest;
complete Euler–Lagrange and constraint-equation ledger;
Dirac/BV/BFV closure;
physical measure;
stress and reaction calculations;
background classification;
radiative-solvability result;
Ward/anomaly interface;
Dynamics certificate.

Non-ownership boundary

Dynamics does not by itself prove:

candidate uniqueness;
intrinsic rigidity;
full physical stability without the Rigidity block;
vacuum-offset protection without the Vacuum block;
local/global fixed-set anomaly closure without the Boundary block.

Observer-response handoff

Dynamics supplies the physical evolution, conserved currents, response functions, and physical measure consumed by OBS. OBS cannot repair an inconsistent Dynamics by projection. Conversely, a lawful parent response cannot be compared with data until OBS has produced the correct record functional.

For time-dependent vacuum tests, Dynamics must evolve the protecting sector and supply the constraint-algebra history required by VAC-C11.

Gauge-owner and kinetic-term consistency

Dynamics consumes the SHP-C09 gauge-owner ledger.

For every surviving generator $T_A$, the parent action must identify exactly one independent connection variable and one owning kinetic structure. Metric Kaluza–Klein notation and principal-bundle notation may describe one field, but the action must not count both as independent unless a second gauge sector is physically intended and appears in the spectrum.

Required checks:

map every gauge-owner ID to a parent-action field;
count independent kinetic operators;
count first-class gauge parameters;
count four-dimensional vector zero modes;
verify equality of these counts after constraints and quotienting;
verify that center/global-lift data is compatible with every charged Actor;
run the duplicate-owner control by treating aliases as independent and confirm that the spectrum gains an extra gauge sector.

A gauge owner with no parent-action term fails Dynamics. A parent-action connection with no Shape owner fails the one-parent audit.

Owned hard constraints and acceptance evidence

The full controlling registry is EVIDENCEDISCHARGEREGISTRYV33_2.md. The rows below are embedded because this block owns or directly co-owns them.

| ID | Required witness | Minimal discharge | Fail trigger | |---|---|---|---| | GEN-C03 | Variational-ownership ledger + equation-disposition table | Every variable is marked varied, gauge, constrained, auxiliary, measured, matching, or external, with the displaced Euler–Lagrange equation explicitly retained, replaced, proved redundant, or abandoned. | A non-varied variable has no lawful equation disposition. | | DYN-C01 | Parent-action manifest + term provenance table | Every primitive term has an owner, support, coefficient provenance, derivative order, symmetry, boundary status, and microscopic/effective label; every gauge connection references exactly one SHP-C09 owner ID. | A matrix element, potential, counterterm, or gauge connection has no parent-action owner, or an owner alias is independently double-counted. | | DYN-C02 | Dirac–Bergmann or BV–BFV closure calculation | All primary/secondary constraints, ranks, brackets, boundary terms, and residual gauges are computed until closure; the rank is constant on the claimed stratum. | The algorithm stops early, the rank changes, or boundary constraints are omitted. | | DYN-C03 | Physical-measure derivation + determinant artifact | The reduced measure includes all Faddeev–Popov/Dirac/BV determinants, and field dependence is retained in loops and matching. | A determinant is dropped as a constant without proof. | | DYN-C04 | Metric variation of all constraint/boundary sectors | The stress tensor is obtained by varying the full action and measure; the result is evaluated on the physical branch. | No-work is used as a substitute for zero stress. | | DYN-C05 | Solvability/Jacobian certificate | The full retained-plus-reaction equation system has a solution and a full-rank Jacobian or a theorem establishes existence in the declared domain. | Radiative normal forces lie outside the multiplier span or the retained equations have no solution. | | DYN-C06 | Ward/BV identity + boundary multiplier ledger | Allowed transformations preserve the domain, all measure anomalies cancel, and multiplier boundary conditions admit a global solution. | A Ward identity, anomaly, or boundary multiplier equation remains unresolved. | | DYN-C07 | Response-function calculation | Localized and nonconstant stress sources produce the correct causal/conservation response while protected constants are handled according to VAC. | The mechanism removes ordinary matter gravity, violates conservation, or produces acausal record response. | | DYN-C08 | Scope theorem or bounded truncation report | The certificate states exactly whether it covers zero modes, a cutoff tower, or all modes, with a tail theorem where a global claim is made. | A local, zero-mode, finite-EFT, or invariant-sector result is promoted beyond scope. | | VAC-C01 | Complete background-equation vector + equation-count/Jacobian report | External, internal, matter, boundary, constraint, and global equations are listed and solved or lawfully replaced; unknown/equation counts and rank are published. | An internal Einstein or boundary equation disappears when a Stage variable is frozen. | | VAC-C04 | Finite constant-shift response experiment | For each protected sector, the full equations are re-solved after $\mathcal Ls o\mathcal Ls-c_s$, and the curvature-record derivative or finite difference is published. | Only an infinitesimal or tree-level shift is tested while auxiliary/global response is held fixed. | | VAC-C06 | Localized-source negative control | Dust, radiation, pressure gradients, and localized stress still source the correct gravitational response. | The protection mechanism degravitates ordinary matter or radiation. | | BND-C03 | Operator-domain certificate | Dirac, gauge, ghost, scalar, and load-bearing graviton domains are self-adjoint/elliptic as required and preserved by gauge/BRST transformations. | A parity table is supplied without a lawful operator domain. | | BND-C07 | Boundary BV/BFV quantum-master-equation output | Ghost, measure, boundary state, and inflow contributions satisfy the relative QME and compose under gluing. | Classical BRST closure is used while the measure/domain anomaly remains. | | VAC-C11 | Time-dependent constraint-algebra and cosmology simulation/theorem | A time-dependent vacuum shift $c(t)$ representing QCD/electroweak transitions is inserted; the constraint algebra remains consistent and the Friedmann/perturbation history stays within frozen bounds, or the regime is explicitly excluded with quantified lost predictions. | The mechanism passes static shifts but becomes singular, acausal, or observationally unacceptable during a finite transition. |

Package status and authority boundary

This file belongs to the Candidate-Neutral Building-Block Authority v3.3.2.

The controlling package authorities are:

EVIDENCEDISCHARGEREGISTRYV33_2.md;
QUANTITATIVESTOPPINGANDEXHAUSTIONRULEV33_2.md;
MANDATORYCONTROLSUITEV33_2.md;
MIGRATIONANDSUPERSESSIONRECORDV3_3.md.

Shared status grammar

PASS:
  The named witness satisfies the minimal discharge criterion.

FAIL:
  A reproducible counterexample or failed acceptance test exists.

OPEN:
  The required witness is missing, incomplete, or inconclusive.

NOT-EVALUATED:
  Evaluation stopped after an earlier hard failure.

NOT-APPLICABLE:
  A type proof establishes that the requirement cannot apply.

CONSTRUCTION-ANCHOR:
  A declared Actor, constraint, boundary term, or global sector realizes
  the result but does not derive it from the pre-existing object.

CONDITIONAL-ON-BND-A:
  The spectrum/domain result awaits fixed-set and operator-domain closure.

CONDITIONAL-ON-BND-B:
  The quantum result awaits local and global anomaly/inflow closure.

RESTART-REQUIRED:
  A frozen object relevant to the result changed.

Universal anti-promotion rules

A bare candidate is not a complete parent object.
A definition is not a witness.
A nonempty equation list is not a solvability proof.
An isolated vacuum is not automatically stable.
A fixed background value is not automatically an absent fluctuation.
Static vacuum-offset protection is not automatically cosmological-history compatibility.
Integrated anomaly cancellation is not local fixed-set cancellation.
Local anomaly cancellation is not global determinant-line trivialization.
A raw higher-dimensional quantity is not automatically the measured four-dimensional observable.
One tested survivor is not a selected survivor without explicit grammar enumeration or a finiteness theorem.

6B.7 Preservation rule for corrected source defects

Two old formulas contained line-wrap corruption in the source Markdown. V4.2 preserves the old source file byte-for-byte in 05_SOURCES/, but the corrected mathematical forms are normative:

\[ S{\mathrm{parent}}=S{\mathrm{grav}}+S{\mathrm{gauge}}+S{\mathrm{matter}}+S{\mathrm{scalar}} +S{\mathrm{boundary}}+S{\mathrm{constraint}}+S{\mathrm{global}}+S_{\mathrm{domain}}, \]

and

\[ D\mu{\mathrm{phys}}=D\mu0\prodA\delta(\XiA)\sqrt{\det C}. \]

No other legacy text is treated as a source defect without a separately hashed correction record.

7. Complete Dynamics constraints

DYN-C01 — Typed parent law and primitive-term ownership

Owned question: What is the complete parent law, and does every primitive term have one lawful owner?

Required inputs: Stage supports; Rulebook permissions; Actor owner IDs; Boundary supports; Scale/provenance packet.

Execution algorithm:

Generate the complete admissible term grammar before reading the gate target.

For every term, record fields, support, tensor contraction, derivative order, symmetry, boundary variation, coefficient provenance, and microscopic/effective status.

Canonicalize aliases and reject duplicate kinetic or interaction owners.

Vary every retained term or provide an explicit non-action replacement with equivalent equation and measure data.

Required outputs: Parent-action manifest; primitive-term ledger; variational-owner ledger; alias/duplicate report.

Minimal discharge: Every primitive term and gauge connection has one lawful owner, support, coefficient provenance, symmetry, derivative order, boundary status, and microscopic/effective scope.

Fail trigger: Unowned terms, double-counted aliases, or a gauge owner without a parent-action term.

Mandatory destructive control: Add an unowned but symmetry-allowed term, or duplicate one connection under metric and bundle notation. The validator must fail.

Gate families invoking this row: Gap-01, Gap-10/BG-10, Gap-11, SG-1, SG-2, SG-3, SG-4, SG-5, SG-7, SG-8, SG-9, UQF-10, UQF-5A/5B, UQF-9, theta-bar-QCD.

Status rule: A definition, qualitative argument, or borrowed terminal is insufficient. Missing gate-scoped evidence is OPEN; a reproducible counterexample is FAIL; NOT-APPLICABLE requires a type proof.

DYN-C02 — Constraint, gauge, and BV/BFV closure

Owned question: Does the constrained system close on the claimed stratum with the correct physical degree count?

Required inputs: Parent equations; constraint candidates; gauge generators; boundary domains; global restrictions.

Execution algorithm:

Run Dirac–Bergmann or BV/BFV closure to termination.

Compute all primary, secondary, and higher constraints and their rank.

Classify first- and second-class sectors, residual gauges, and boundary constraints.

Recompute physical degree counts on every rank stratum used by the claim.

Required outputs: Constraint algebra; bracket matrix; rank-stratum table; residual-gauge ledger; physical degree count.

Minimal discharge: All constraints, ranks, brackets, residual gauges, boundary terms, and physical degree counts are computed to closure on the claimed stratum.

Fail trigger: Early termination, rank change, omitted boundary constraint, or unresolved residual gauge.

Mandatory destructive control: Perturb to a rank-changing stratum or remove a boundary constraint. The claimed branch must reopen.

Gate families invoking this row: SG-2, UQF-10.

DYN-C03 — Physical measure and determinant ownership

Owned question: What measure lives on the reduced physical space, and which determinants contribute to loops, matching, and stress?

Required inputs: Constraint algebra; gauge fixing; field domains; boundary/ghost sectors.

Execution algorithm:

Derive FP, Dirac, BV, and boundary determinants.

Test whether each determinant is field dependent.

Carry field-dependent terms into the effective action, stress, anomaly, and matching calculations.

Publish regulator, phase, zero-mode, and normalization treatment.

Required outputs: Physical-measure packet; determinant ledger; effective-action contribution table.

Minimal discharge: All FP/Dirac/BV determinants and field dependence are retained in loops, matching, and stress calculations.

Fail trigger: A determinant is dropped as a constant without proof.

Mandatory destructive control: Drop a field-dependent determinant as normalization. The audit must produce a different loop or anomaly result and fail.

Gate families invoking this row: Born-rule, Gap-01, Gap-05-stability, Gap-13, SG-4, SG-7, UQF-3, UQF-4, UQF-5A/5B, UQF-7, UQF-9.

DYN-C04 — Full stress and metric-response derivation

Owned question: What stress is produced by every parent, constraint, boundary, ghost, and reaction sector?

Required inputs: Complete action/measure; solved multipliers; metric and boundary variations.

Execution algorithm:

Vary the full action and physical measure with respect to the metric.

Include volume-form, explicit metric, solved-multiplier, determinant, and boundary contributions.

Separate no-work statements from stress statements.

Evaluate on the lawful branch and compare constant versus localized sources.

Required outputs: Stress tensor decomposition; reaction-stress ledger; constant/nonconstant response split.

Minimal discharge: Stress is derived from the complete action and measure, including constraints, boundaries, ghosts, and solved multiplier dependence.

Fail trigger: No-work or absence from a propagator is substituted for zero stress.

Mandatory destructive control: Use a metric-dependent ideal constraint with zero virtual work but nonzero stress. No-work must not pass as zero-stress evidence.

Gate families invoking this row: Gap-05-stability, Lambda-catastrophe.

DYN-C05 — Retained-plus-reaction solvability and background closure

Owned question: Do all retained, constrained, global, and boundary equations admit a lawful solution?

Required inputs: Complete equation vector; constraint reactions; global variables; boundary equations.

Execution algorithm:

Count independent unknowns and equations after identities.

Construct the coupled retained-plus-reaction system.

Compute the Jacobian/Fredholm map or invoke an existence theorem with declared hypotheses.

Classify the result as parent solution, constrained-reaction solution, effective external background, or inconsistent background.

Required outputs: Equation ledger; unknown/equation count; solvability/Jacobian certificate; background classification.

Minimal discharge: The complete coupled equations have a solution with full-rank Jacobian or an existence theorem on the declared domain.

Fail trigger: Normal forces lie outside multiplier span or retained equations are unsolved.

Mandatory destructive control: Choose a radiative normal force outside the multiplier span. A no-propagator claim must still fail solvability.

Gate families invoking this row: Gap-05-stability, Lambda-catastrophe, SG-1, SG-5, SG-6, UQF-10, theta-bar-QCD.

DYN-C06 — Ward, anomaly, domain, and global quantum consistency

Owned question: Do gauge/BRST/BV identities survive the measure, boundaries, fixed sets, and global gluing?

Required inputs: Physical measure; domains; anomaly polynomials; boundary and inflow data; global-form data.

Execution algorithm:

Compute allowed transformations preserving every domain.

Evaluate bulk, fixed-set, ghost, measure, counterterm, and inflow variations in one convention.

Check local cancellation on every stratum and relative/global determinant-line trivialization.

Verify the quantum master equation and gluing compatibility.

Required outputs: Ward/BV packet; local anomaly ledger; inflow/quantization packet; relative-QME result.

Minimal discharge: The domain is preserved, anomalies cancel, and multiplier/boundary equations admit a global solution.

Fail trigger: Unresolved Ward identity, anomaly, boundary equation, or QME residual.

Mandatory destructive control: Arrange integrated anomaly cancellation while one fixed-set residual remains. The gate must stay open.

Gate families invoking this row: Born-rule, Gap-01, SG-2, SG-3, SG-4, SG-9, UQF-3, UQF-4, UQF-5C, UQF-7, UQF-9, theta-bar-QCD.

DYN-C07 — Physical response, conservation, and ordinary-source control

Owned question: How does the lawful system respond to localized and nonconstant sources without losing conservation or causality?

Required inputs: Solved background; physical operators; currents; Observer/TS interfaces; Vacuum packet where relevant.

Execution algorithm:

Derive retarded/causal response functions on the physical quotient.

Track exact currents and exchange terms.

Apply localized dust, radiation, pressure-gradient, and wave-packet controls.

Separate protected constants from ordinary excitations and publish record-level response.

Required outputs: Response-function packet; current-conservation ledger; ordinary-source negative control.

Minimal discharge: Localized and nonconstant sources yield the correct conserved causal response while protected constants follow VAC.

Fail trigger: Ordinary matter is degravitated, conservation fails, or response is acausal.

Mandatory destructive control: Project out all trace and traceless stress. Constant-shift protection may pass, but ordinary gravity must fail.

Gate families invoking this row: Black-hole-singularity, Born-rule, Gap-02, Gap-05-stability, Gap-05-value, Gap-08, Gap-10/BG-10, Gap-11, Gap-13, Lambda-catastrophe, UQF-14, UQF-5A/5B.

DYN-C08 — Scope, tower, and anti-promotion theorem

Owned question: What exact modal, energy, time, and approximation scope is proven?

Required inputs: Operator spectra; cutoff; Granularity inventory; Scale packet; tail information.

Execution algorithm:

Declare zero-mode, finite-tower, EFT, history-window, or all-mode scope.

List unresolved modes, sectors, and time intervals.

Supply a tail theorem or bounded remainder for any global claim.

Block every promotion from finite evidence to a stronger terminal.

Required outputs: Scope theorem; truncation ledger; tail/remainder certificate; claim ceiling.

Minimal discharge: The result declares zero-mode, finite-tower, EFT, or all-mode scope, with a tail theorem for global claims.

Fail trigger: A local or finite result is promoted beyond scope.

Mandatory destructive control: Use a finite prefix with two lawful tails giving opposite global behavior. The global claim must fail.

Gate families invoking this row: Black-hole-singularity, Gap-01, Gap-02, Gap-05-stability, Gap-13, SG-1, SG-10, SG-2, SG-3, SG-6, SG-7, SG-8, SG-9, UQF-10, UQF-14, UQF-3, UQF-5A/5B, UQF-5C, UQF-9.

DYN-C09 — Physical operator, kernel, spectrum, and response construction

Owned question: What physical operators follow from the complete equations, and what kernels and spectra survive every quotient and domain?

Required inputs: Solved background; full equations; constraint/gauge complex; Boundary domains; Actor owners; Granularity scope.

Execution algorithm:

Generate every gate-relevant fluctuation sector from the Stage–Actor support grammar.

Linearize the full equations, including mixed blocks and reaction sectors.

Apply gauge fixing, constraints, boundary/global domains, and physical projectors.

Publish raw, gauge, constrained, and physical kernels; zero modes; generalized modes; massive spectrum; response functions; and unresolved tails.

Prove operator-shelf saturation: every generated carrier/operator has one disposition.

Required outputs: Physical-operator packets; mixed-block matrix; kernel/spectrum ledger; operator-saturation certificate.

Minimal discharge: Linearize the complete parent equations, build the gauge-fixed and constraint-reduced operators on the lawful domains, and publish kernels, zero modes, spectra, response functions, multiplicities, and unresolved tails.

Fail trigger: A gate uses a declared Actor or expected spectrum without deriving the corresponding physical operator/kernel, or omits a mixed/operator block.

Mandatory destructive control: Add one lawful boundary-localized zero mode while keeping the owner list unchanged. The no-extra claim must fail.

Gate families invoking this row: Black-hole-singularity, Gap-01, Gap-02, Gap-08, SG-1, SG-10, SG-2, SG-3, SG-5, SG-6, SG-8, UQF-10, UQF-14, UQF-3, UQF-5A/5B, UQF-7, UQF-9.

DYN-C10 — Complete interaction, source, and dangerous-operator hypergraph

Owned question: What are all lawful interactions and sources, including theorem-zero and dangerous channels?

Required inputs: Parent term grammar; Actor/Co-Actor registry; Rulebook representation and selection rules; Boundary/Scale data.

Execution algorithm:

Generate all arity-1 and higher hyperedges allowed by support, representation, tensor, parity, charge, and derivative grammar.

Map every edge to a parent owner or a theorem-zero exclusion.

Track radiative generation, dangerous operators, portals, CP sources, baryon/lepton/flavor charges, and Observer records.

Run edge saturation and omitted-edge controls before evaluating the target gate.

Required outputs: Interaction hypergraph; theorem-zero ledger; dangerous-operator roster; edge-saturation certificate.

Minimal discharge: Enumerate every parent-owned interaction vertex, source edge, representation contraction, selection rule, theorem-zero edge, dangerous operator, support, scale, and boundary domain.

Fail trigger: A coupling, decay, portal, Yukawa, CP source, or dangerous operator is inserted or omitted without a complete parent-law disposition.

Mandatory destructive control: Hold the free spectrum fixed and add one allowed cubic/Yukawa edge to one candidate. Interaction-dependent gates must distinguish them.

Gate families invoking this row: Gap-10/BG-10, Gap-11, SG-5, SG-7, SG-8, SG-9, UQF-10, theta-bar-QCD.

DYN-C11 — Mass, mixing, transition, decay, and threshold derivation

Owned question: Do physical masses and transitions follow from owned interactions on a solved background?

Required inputs: Interaction hypergraph; background/order parameters; kinetic normalization; Scale/matching packet.

Execution algorithm:

Evaluate interaction derivatives on the solved background.

Construct kinetic and mass/mixing blocks after constraints and boundary reductions.

Canonically normalize, diagonalize, and identify physical eigenstates.

Derive widths, transition amplitudes, thresholds, and effective vertices with uncertainty and scope.

Run zero-condensate, wrong-representation, duplicate-owner, and omitted-edge controls.

Required outputs: Mass/mixing packet; eigenstate map; transition/decay ledger; threshold packet.

Minimal discharge: Mass matrices, mixings, symmetry breaking, decay widths, threshold transitions, and effective vertices are derived from C10 plus the solved background and are diagonalized/matched with stated scope.

Fail trigger: A matrix or transition is supplied by hand, the background does not solve the parent equations, or physical eigenstates/widths are not derived.

Mandatory destructive control: Insert a phenomenologically correct matrix without a parent vertex or solved order parameter. The row must fail.

Gate families invoking this row: Gap-10/BG-10, Gap-11, SG-5, SG-8, SG-9, theta-bar-QCD.

DYN-C12 — Quantum physicality, positivity, poles, and analytic continuation

Owned question: Does the quantum theory possess a positive physical sector with lawful continuation and pole structure?

Required inputs: Physical measure; gauge/BRST quotient; Euclidean/Lorentzian operator; domains; regulator family.

Execution algorithm:

Construct the physical pairing after quotient.

Test reflection positivity or an equivalent reconstruction theorem in the declared formalism.

Continue with an explicit prescription and track domains and branch cuts.

Compute physical poles, residues, complex modes, and negative-norm dispositions.

Repeat over required regulator/truncation families.

Required outputs: Quantum-physicality packet; reconstruction/positivity certificate; pole-residue ledger.

Minimal discharge: After gauge/BRST quotient, establish a positive physical pairing or reflection-positivity/equivalent reconstruction, pole and residue signs, continuation prescription, and absence/disposition of negative-norm states.

Fail trigger: Formal self-adjointness, Euclidean convergence, or BRST nilpotency is used without a physical positivity/pole certificate.

Mandatory destructive control: Use a formally self-adjoint gauge-fixed operator with a negative-residue physical pole. Self-adjointness alone must fail.

Gate families invoking this row: Born-rule, Gap-02, Gap-13, SG-5, SG-6, SG-8, UQF-10, UQF-14, UQF-3, UQF-5A/5B, UQF-5C.

DYN-C13 — Closed/open quantum evolution and probability instruments

Owned question: Is probability evolution lawful for closed and open sectors, including entangled extensions and Observer records?

Required inputs: Physical Hilbert/record spaces; Hamiltonian or channel generator; environment/interface ledger; Observer map.

Execution algorithm:

For closed sectors, prove unitary normalized evolution on the physical domain.

For open sectors, define the system–environment split, exchange currents, and CPTP channel or justified instrument.

Check complete positivity on admitted ancillas and composition across time/interface cuts.

Publish approximation errors and record normalization.

Required outputs: Quantum-channel packet; instrument/POVM packet; environment and exchange-current ledger.

Minimal discharge: Closed sectors have unitary normalized evolution; open sectors publish a completely positive trace-preserving channel or justified instrument, environment, exchange currents, approximation bound, and Observer handoff.

Fail trigger: A trace-preserving but nonphysical map, unnormalized probability rule, undeclared environment, or hidden information loss is used.

Mandatory destructive control: Use a trace-preserving but non-completely-positive map. Normalization must not be accepted as physical evolution.

Gate families invoking this row: Born-rule, Gap-10/BG-10, Gap-11, Gap-13, UQF-14, UQF-3.

DYN-C14 — Nonequilibrium, thermal, and cosmological-history evolution

Owned question: Does the proposed mechanism work through finite-time thermal and cosmological history?

Required inputs: Initial state/ensemble; background expansion; interaction graph; transport/collision data; Vacuum/Observer packets.

Execution algorithm:

Specify the initial ensemble and history interval.

Choose and justify Boltzmann, Schwinger–Keldysh, transport, lattice, kinetic, or equivalent evolution.

Compute production, washout, freeze-in/out, entropy, charge, perturbation, and transition histories.

Propagate uncertainties and compare finite records.

Separate static identities from history claims.

Required outputs: Nonequilibrium-history packet; abundance/charge trajectories; transition and perturbation records.

Minimal discharge: Publish initial state, thermal/kinetic/transport equations, entropy and charge production, phase-transition dynamics, production/washout/freeze-out, perturbations, and uncertainty through the claimed history.

Fail trigger: A static potential or constant-shift result is promoted to a finite-time cosmological, baryogenesis, dark-matter, or transition claim.

Mandatory destructive control: Use a mechanism that cancels static constants but produces an unacceptable transient. Static success must not close the history gate.

Gate families invoking this row: Gap-05-stability, Gap-05-value, Gap-08, Gap-10/BG-10, Gap-11, Lambda-catastrophe, theta-bar-QCD.

DYN-C15 — Well-posed causal initial-boundary-value evolution

Owned question: Do the equations define unique, stable, constraint-preserving predictions on the declared causal support?

Required inputs: Complete equations; principal symbol; initial surfaces; Boundary domains; TS and Observer handoffs.

Execution algorithm:

Compute the principal symbol or equivalent propagation object.

Establish hyperbolicity/well-posedness or a formalism-appropriate substitute.

Specify admissible initial data and boundary/fixed-set data.

Prove constraint propagation, uniqueness, continuous dependence, and support/no-signalling.

Compose clocks and interfaces through TS.

Required outputs: Causal-IBVP packet; characteristic-cone ledger; constraint-propagation certificate.

Minimal discharge: Prove or compute hyperbolicity/evolution well-posedness, constraint propagation, boundary compatibility, causal support, stability under allowed data, and synchronization/Observer handoffs.

Fail trigger: Equations exist but evolution is nonunique, unstable, superluminal outside the declared cone, domain-incompatible, or not globally composable.

Mandatory destructive control: Supply complete formal equations with nonunique evolution or non-preserved constraints. Equation completeness alone must fail.

Gate families invoking this row: Black-hole-singularity, Gap-02, Gap-08, Gap-10/BG-10, Gap-13, SG-1, SG-6, UQF-14, UQF-3, UQF-5A/5B, UQF-5C.

Owned question: Does the result survive lawful enlargement of operator bases, resolutions, schemes, and regulators?

Required inputs: Nested theory spaces; generated operators; regulators/schemes; Scale/Granularity packets.

Execution algorithm:

Construct nested operator bases or refinements before target inspection.

Track generated operators and closure residuals at every level.

Compute observables/flows/fixed points and differences between levels.

Vary admissible regulator and scheme families.

Provide convergence, critical-data, matching, and omitted-tail evidence.

Required outputs: RG/refinement packet; convergence table; scheme/regulator stability certificate.

Minimal discharge: Use nested operator bases/resolutions and admissible regulator/scheme families; track generated operators, fixed points/flows, critical data, convergence, matching, and omitted-tail bounds.

Fail trigger: A result exists only in one truncation, basis, regulator, or scheme and changes materially under lawful refinement.

Mandatory destructive control: Choose two lawful higher-order completions sharing the finite prefix but with opposite fixed-point behavior. A completion claim must fail.

Gate families invoking this row: Gap-01, Gap-02, Gap-05-stability, Gap-08, Gap-11, Gap-13, Lambda-catastrophe, SG-10, SG-6, SG-7, SG-8, SG-9, UQF-10, UQF-14, UQF-3, UQF-5A/5B, UQF-5C, UQF-9, theta-bar-QCD.

DYN-C17 — Regional, horizon, interface, and information-flux balance

Owned question: How do conserved quantities and information move across boundaries, horizons, defects, or coarse-graining cuts?

Required inputs: Global currents; region/interface geometry; Boundary/TS/Observer data; open-system packet.

Execution algorithm:

Define the region, interface, normals, and edge sectors.

Derive energy, charge, probability, entropy, and information balance laws.

Include boundary, horizon, gluing, environment, and edge contributions.

Distinguish global conservation from regional change and apparent subsystem nonunitarity.

Required outputs: Regional-flux packet; interface/gluing ledger; information-channel balance.

Minimal discharge: For regions separated by boundaries, defects, horizons, or cuts, publish charge/energy/probability/information currents, gluing law, edge terms, exchange channel, and finite Observer records.

Fail trigger: Local conservation is claimed while flux through an interface is omitted, or subsystem nonunitarity is mistaken for global loss without a channel ledger.

Mandatory destructive control: Omit flux through a horizon while retaining local conservation. The regional closure must fail.

Gate families invoking this row: Black-hole-singularity, Gap-13, UQF-14.

8. Full packet schemas

8.1 `parentactionmanifest`

parent_action_manifest:

  manifest_id:

  branch_id:

  fields:

  supports:

  terms:

  coefficient_provenance:

  symmetries:

  boundary_variations:

  variational_dispositions:

  aliases:

  generated_term_grammar:

  omitted_term_theorem:

  status:

8.2 `constraintclosurepacket`

constraint_closure_packet:

  constraint_ids:

  primary_constraints:

  secondary_constraints:

  brackets:

  rank_strata:

  first_class:

  second_class:

  residual_gauges:

  boundary_constraints:

  physical_dof_count:

  termination_proof:

  status:

8.3 `physicalmeasurepacket`

physical_measure_packet:

  measure_id:

  gauge_fixing:

  ghosts:

  fp_determinant:

  dirac_determinant:

  bv_bfv_measure:

  zero_modes:

  phases:

  field_dependence:

  effective_action_terms:

  stress_terms:

  status:

8.4 `backgroundsolvabilitypacket`

background_solvability_packet:

  unknowns:

  equations:

  identities:

  gauge_freedoms:

  boundary_global_equations:

  jacobian_or_fredholm_map:

  existence_domain:

  solution:

  classification:

  residuals:

  status:

8.5 `physicaloperatorpacket`

physical_operator_packet:

  operator_id:

  parent_equations:

  background:

  carrier_and_owner:

  raw_operator:

  mixed_blocks:

  constraint_complex:

  gauge_fixing:

  boundary_global_domain:

  physical_projector:

  raw_kernel:

  gauge_kernel:

  physical_kernel:

  zero_modes:

  spectrum:

  response:

  tail_certificate:

  status:

8.6 `interactionhypergraphpacket`

interaction_hypergraph_packet:

  edge_generator:

  actor_vertices:

  composite_vertices:

  edges:

  representation_contractions:

  charges:

  parities:

  supports:

  selection_rules:

  radiative_generation:

  dangerous_operators:

  theorem_zero_edges:

  omitted_edge_theorem:

  status:

8.7 `massmixingtransition_packet`

mass_mixing_transition_packet:

  background_order_parameters:

  kinetic_matrix:

  mass_matrix:

  mixing_blocks:

  normalization:

  eigenstates:

  eigenvalues:

  transition_amplitudes:

  decay_widths:

  thresholds:

  uncertainties:

  controls:

  status:

8.8 `quantumphysicalitypacket`

quantum_physicality_packet:

  formalism:

  physical_quotient:

  pairing:

  reflection_positivity:

  reconstruction:

  continuation:

  poles:

  residues:

  branch_cuts:

  negative_norms:

  complex_modes:

  regulator_scope:

  status:

8.9 `quantumchannelpacket`

quantum_channel_packet:

  closed_or_open:

  system_space:

  environment_space:

  generator_or_unitary:

  channel_or_instrument:

  complete_positivity:

  trace_normalization:

  exchange_currents:

  composition:

  observer_records:

  approximation_bound:

  status:

8.10 `nonequilibriumhistorypacket`

nonequilibrium_history_packet:

  initial_state:

  ensemble:

  time_interval:

  temperature_history:

  expansion_history:

  evolution_equations:

  collision_terms:

  sources:

  entropy:

  charges:

  production:

  washout:

  freeze_in_out:

  perturbations:

  records:

  uncertainty:

  status:

8.11 `causalinitialboundary_packet`

causal_initial_boundary_packet:

  principal_symbol:

  characteristics:

  causal_structure:

  initial_surface:

  initial_data:

  boundary_data:

  constraint_propagation:

  existence:

  uniqueness:

  continuous_dependence:

  support:

  ts_handoff:

  observer_handoff:

  status:

8.12 `rgrefinementpacket`

rg_refinement_packet:

  nested_spaces:

  generated_operators:

  regulators:

  schemes:

  flows:

  fixed_points:

  critical_data:

  observables:

  level_differences:

  convergence:

  matching:

  tail_bounds:

  status:

8.13 `regionalfluxpacket`

regional_flux_packet:

  region:

  interfaces:

  normals:

  currents:

  edge_terms:

  gluing:

  environment_channels:

  energy_balance:

  charge_balance:

  probability_balance:

  entropy_balance:

  information_balance:

  observer_records:

  status:

8.14 `integrateddynamicscertificatev42`

This is the required top-level gate handoff. It preserves the complete V3 view and binds every V4.2 packet to one branch, gate, scope, and calculation order.

integrated_dynamics_certificate_v4_2:
  candidate_id:
  branch_id:
  gate_id:
  authority_hashes: {}
  frozen_assumptions: []
  legacy_v3_compatibility:
    parent_action:
    primitive_term_ledger:
    complete_equation_vector:
    equation_count_and_identities:
    constraint_types:
    dirac_bergmann_closure:
    rank_strata:
    physical_measure:
    determinant_contributions:
    constraint_stress:
    multiplier_boundary_problem:
    background_status:
    background_solution:
    radiative_solvability:
    ward_identities:
    anomaly_result:
    physical_hessian_packet:
    vacuum_response_packet:
    ordinary_gravity_control:
    phase_transition_scope:
    full_tower_scope:
    evidence_hashes: []
    verdict:
  packets:
    parent_action_manifest:
    constraint_closure_packet:
    physical_measure_packet:
    background_solvability_packet:
    physical_operator_packet:
    interaction_hypergraph_packet:
    mass_mixing_transition_packet:
    quantum_physicality_packet:
    quantum_channel_packet:
    nonequilibrium_history_packet:
    causal_initial_boundary_packet:
    rg_refinement_packet:
    regional_flux_packet:
    boundary_quantum_dynamics:
  legacy_negative_controls:
    no_propagator_but_no_solution:
    no_work_but_nonzero_stress:
    vacuum_protection_but_matter_degravitation:
    frozen_stage_with_abandoned_equations:
  v4_2_destructive_controls: []
  residual_vector: {}
  claim_ceiling:
  physical_verdict:
  dynamics_sufficiency_verdict:
  project_dependency_verdict:
  reopen_triggers: []
  stale_dependencies: []
  calculation_order:
  validator_result:
  evidence_hashes: []

A gate may publish specialized subcertificates, but this integrated certificate is mandatory for a final Dynamics adjudication.

9. Candidate generation and saturation algorithms

9.1 Parent-term saturation

INPUT: frozen Stage, Rulebook, Actor, Scale, Boundary scope
1. Enumerate supports, fields/owners, tensor types, representations, derivative orders, strata, and global classes.
2. Form every invariant local/global/boundary monomial allowed by the grammar.
3. Canonicalize integrations by parts, identities, field redefinitions, cover/quotient aliases, and exact equivalences.
4. Assign owner, coefficient provenance, and disposition: retained / forbidden / theorem-zero / matching-only / open.
5. Repeat after radiative generation and refinement.
PASS only when no undisposed in-grammar term remains.

9.2 Operator-shelf saturation

For every Stage-supported Actor carrier and every lawful mixed pair:
  derive the complete linearized block from the full equations;
  attach constraint, gauge, boundary, global, and physical-pairing data;
  compute or theorem-classify kernel and spectrum;
  assign every zero/generalized/massive mode and unresolved tail;
  compare against Granularity mode inventory.
PASS only when generated operators and modes have one terminal disposition.

9.3 Interaction-edge saturation

Generate every hyperedge from Actor tuples, representation singlets, support overlap, parity, exact charges, derivative grammar, and Rulebook permissions.
For each edge, prove parent ownership, theorem-zero exclusion, or OPEN status.
Run dangerous-operator and radiative-generation closure.
PASS only when a new generation pass adds no inequivalent edge.

9.4 History/refinement saturation

Refine modal cutoff, operator basis, regulator/scheme, time resolution, thermal species, regional decomposition, and interface data.
Track observable and terminal changes.
PASS for a global claim only with convergence/tail theorem; otherwise emit the strongest finite-scope terminal.

10. Thought-experiment derivation and destructive controls

TE-DYN-01 → `DYN-C09`

Same owner/action labels, but one candidate has an extra boundary zero mode. The old rows can pass while the physical result changes; therefore DYN-C09 is irreducible under the current grammar.

TE-DYN-02 → `DYN-C10`

Identical quadratic theories, but only one has an allowed cubic or Yukawa vertex. The old rows can pass while the physical result changes; therefore DYN-C10 is irreducible under the current grammar.

TE-DYN-03 → `DYN-C11`

A correct-looking mass matrix is inserted with no parent vertex or solved condensate. The old rows can pass while the physical result changes; therefore DYN-C11 is irreducible under the current grammar.

TE-DYN-04 → `DYN-C12`

A formally self-adjoint gauge-fixed operator has a negative physical residue. The old rows can pass while the physical result changes; therefore DYN-C12 is irreducible under the current grammar.

TE-DYN-05 → `DYN-C13`

A trace-preserving subsystem map fails complete positivity on an entangled extension. The old rows can pass while the physical result changes; therefore DYN-C13 is irreducible under the current grammar.

TE-DYN-06 → `DYN-C14`

A static vacuum cancellation produces an unacceptable finite-time transient. The old rows can pass while the physical result changes; therefore DYN-C14 is irreducible under the current grammar.

TE-DYN-07 → `DYN-C15`

A complete equation list has nonunique or constraint-violating evolution. The old rows can pass while the physical result changes; therefore DYN-C15 is irreducible under the current grammar.

TE-DYN-08 → `DYN-C16`

A fixed point disappears under a lawful higher-order completion. The old rows can pass while the physical result changes; therefore DYN-C16 is irreducible under the current grammar.

TE-DYN-09 → `DYN-C17`

Local conservation is claimed while horizon/interface flux is omitted. The old rows can pass while the physical result changes; therefore DYN-C17 is irreducible under the current grammar.

The original controls remain mandatory: unowned term, early constraint termination, dropped determinant, no-work/zero-stress substitution, unsolved reaction system, integrated-only anomaly cancellation, ordinary-source degravitation, and finite-to-global scope promotion.

11. Gate execution compiler

11.1 Frozen audit

Load gate contract, authorities, hashes, scope, expected witness types, and allowed terminals.
Select every revised Dynamics row from the gate profile; NOT-APPLICABLE requires a type proof.
Build the parent-term, equation, constraint, operator, interaction, and history slices without reading the desired answer.
Evaluate row by row and freeze PASS/FAIL/OPEN plus evidence hashes.
Run all mandatory destructive controls.
Compute the Dynamics residual vector.

11.2 Repair loop

Repairs occur only after the immutable audit. A repair is admissible only if it is candidate-neutral, reusable across every gate invoking the row, does not add a target-driven Actor/term/constraint/regulator, and propagates through dependency hashes. Re-execute from the earliest changed pass.

11.3 Challenge calculation

Every gate must include one calculation capable of falsifying the current branch or improving a reusable building block. A challenge calculation is not a prose review. It must produce machine-readable inputs, code/order, outputs, controls, and residuals.

11.4 Terminal separation

Physical endpoint: what the calculation actually establishes.
Dynamics sufficiency endpoint: whether this block had all required capabilities.
Project-dependency endpoint: whether the scoped gate dependency is resolved under governance.
Frontier/external endpoint: any unsolved theorem, measurement, or UV completion wall.

12. All-gate Dynamics profiles

12.1 `Black-hole-singularity`

Dynamics role: LOAD-BEARING. Source terminal under test: DISSOLVED-GIVEN-root / RESOLVED +0. Required rows: DYN-C07, DYN-C08, DYN-C09, DYN-C15, DYN-C17.

Audit finding: Dissolving a continuum singularity does not supply a finite causal evolution, horizon/interface flux balance, or record map.

Required execution:

construct physical gravitational operator and regularized/finite-support kernel at claimed scope.

establish causal evolution on the non-continuum interior model.

publish horizon/interface flux and Observer-record packet.

Claim ceiling / action: Add C15/C17 and integrate TS/OBS; no claim of a UV interior solution.

Minimum destructive controls: run the controls attached to every selected row, plus omitted-parent-term, omitted-operator/mode, omitted-interaction-edge, and scope-promotion controls where type-applicable.

12.2 `Born-rule`

Dynamics role: LOAD-BEARING. Source terminal under test: CLOSED / CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C03, DYN-C06, DYN-C07, DYN-C12, DYN-C13.

Audit finding: A stronger Born derivation requires a positive physical measure and lawful normalized event instrument; the current irreducibility terminal can remain narrower.

Required execution:

derive positive physical measure and quotient.

construct normalized event instrument or identify irreducible operational anchor.

run non-CP and normalization destructive controls.

Claim ceiling / action: Genuine improvement for constructive derivation; no forced change to irreducibility terminal.

12.3 `Gap-01`

Dynamics role: LOAD-BEARING. Source terminal under test: DERIVED-GIVEN-anchor / RESOLVED +0. Required rows: DYN-C01, DYN-C03, DYN-C06, DYN-C08, DYN-C09, DYN-C16.

Audit finding: The a6 coefficient depends on the complete operator, domain, measure, boundary data, scheme, and finite-order scope.

Required execution:

build complete Laplace-type operator and boundary domain.

include ghosts/measure and anomaly conventions.

calculate finite heat-kernel coefficient at declared order and test scheme/refinement scope.

Claim ceiling / action: Add generic operator/kernel and refinement certificates; calculation remains gate-specific.

12.4 `Gap-02`

Dynamics role: LOAD-BEARING. Source terminal under test: CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C07, DYN-C08, DYN-C09, DYN-C12, DYN-C15, DYN-C16.

Audit finding: A mass-gap claim requires a physical spectral operator, positive physical sector, causal theory, and nonperturbative/refinement control. The external-wall terminal needs only proof that these are not supplied.

Required execution:

construct physical Yang–Mills spectral operator.

establish positive physical sector and causal dynamics.

supply nonperturbative/refinement evidence or issue external-wall terminal.

Claim ceiling / action: Add C09/C12/C15/C16; no claim that the Clay problem is solved.

12.5 `Gap-05-stability`

Dynamics role: LOAD-BEARING. Source terminal under test: CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C03, DYN-C04, DYN-C05, DYN-C07, DYN-C08, DYN-C14, DYN-C16.

Audit finding: Radiative stability requires full measure/stress, solvable reactions, ordinary-source control, time-dependent transitions, and scheme/refinement stability.

Required execution:

derive full vacuum/reaction stress and radiative equations.

simulate finite-time phase transitions.

test regulator/scheme/refinement stability.

Claim ceiling / action: Add C14/C16 execution; VAC retains vacuum-specific ownership.

12.6 `Gap-05-value`

Dynamics role: NOT-LOAD-BEARING-FOR-MEASURED-TERMINAL. Source terminal under test: MEASURED-ANCHOR / RESOLVED +0. Required rows: DYN-C07, DYN-C14.

Audit finding: The measured value terminal does not require a mechanism. A predictive/history claim does require response and cosmological evolution.

Required execution:

for measured terminal, verify ordinary response and history compatibility only.

for predictive terminal, derive mechanism and cosmological evolution.

Claim ceiling / action: No change for measured anchor; use C14 only for stronger claim.

12.7 `Gap-08`

Dynamics role: LOAD-BEARING. Source terminal under test: DISSOLVED-GIVEN-root / RESOLVED +0. Required rows: DYN-C07, DYN-C09, DYN-C14, DYN-C15, DYN-C16.

Audit finding: Replacing or dissolving inflation still requires a complete causal perturbation/history map from initial data to finite records.

Required execution:

specify initial state and causal perturbation evolution.

derive record map replacing inflationary history.

test refinement and uncertainty.

Claim ceiling / action: Genuine improvement: nonequilibrium history and causal evolution packets.

12.8 `Gap-10/BG-10`

Dynamics role: LOAD-BEARING. Source terminal under test: CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C01, DYN-C07, DYN-C10, DYN-C11, DYN-C13, DYN-C14, DYN-C15.

Audit finding: Baryogenesis requires CP-violating interactions, out-of-equilibrium transport, charge/entropy evolution, washout, freeze-out, and causal initial data.

Required execution:

generate CP-violating interaction hypergraph.

derive kinetic/transport equations and charge sources.

compute production, washout, freeze-out, and final asymmetry.

Claim ceiling / action: Genuine Dynamics improvement: interaction plus nonequilibrium/thermal module.

12.9 `Gap-11`

Dynamics role: LOAD-BEARING. Source terminal under test: CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C01, DYN-C07, DYN-C10, DYN-C11, DYN-C13, DYN-C14, DYN-C16.

Audit finding: A dark-matter portal needs complete production/decay interactions, open/thermal evolution, abundance history, and running/matching.

Required execution:

generate portal/production/decay edges.

derive thermal/open-system abundance evolution.

run matching and RG stability.

Claim ceiling / action: Genuine Dynamics improvement: interaction and thermal production module.

12.10 `Gap-13`

Dynamics role: LOAD-BEARING. Source terminal under test: CLOSED / PROJECT-DEPENDENCY / CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C03, DYN-C07, DYN-C08, DYN-C12, DYN-C13, DYN-C15, DYN-C16, DYN-C17.

Audit finding: Microstate/Page claims require positive quantum evolution, subsystem channels, causal/horizon flux, refinement scope, and finite records.

Required execution:

construct positive quantum channel for horizon-separated regions.

track Page/information and energy flux.

state refinement/UV claim ceiling.

Claim ceiling / action: Add quantum physicality, open-system, causal, and horizon-flux interfaces; constructive QG remains external.

12.11 `Lambda-catastrophe`

Dynamics role: LOAD-BEARING. Source terminal under test: DISSOLVED-GIVEN-root / RESOLVED +0. Required rows: DYN-C04, DYN-C05, DYN-C07, DYN-C14, DYN-C16.

Audit finding: A degravitation mechanism must solve full equations, retain ordinary gravity, survive phase transitions, and remain radiatively stable.

Required execution:

solve complete reaction/background equations.

retain ordinary localized gravity.

simulate finite vacuum transitions and radiative stability.

Claim ceiling / action: Add C14/C16; VAC remains the mechanism owner.

12.12 `SG-1`

Dynamics role: SUPPORTING. Source terminal under test: CLOSED / DERIVED-GIVEN-SHAPE / RESOLVED +0. Required rows: DYN-C01, DYN-C05, DYN-C08, DYN-C09, DYN-C15.

Audit finding: Existing Shape terminal does not require a derived parent vacuum, but any stronger claim that the selected Stage is dynamically realized requires background solvability, physical operators, and well-posed evolution.

Required execution:

for stronger dynamical-realization claim, solve parent background.

construct geometric fluctuation operators.

prove causal/well-posed evolution at declared scope.

Claim ceiling / action: Crosswalk expansion only; no new gate-specific physics term.

12.13 `SG-10`

Dynamics role: LOAD-BEARING. Source terminal under test: DERIVED-GIVEN-anchor / RESOLVED +0. Required rows: DYN-C08, DYN-C09, DYN-C16.

Audit finding: Scope consistency requires the actual operator/tower content and a refinement/tail certificate, not a label saying finite or all modes.

Required execution:

construct actual tower operator and mode inventory.

publish tail theorem or finite scope.

test refinement stability.

Claim ceiling / action: Add C09/C16 to make the existing anti-promotion rule executable.

12.14 `SG-2`

Dynamics role: LOAD-BEARING. Source terminal under test: CLOSED / CERTIFIED-IRREDUCIBLE-CATEGORY-FLOOR / RESOLVED +0. Required rows: DYN-C01, DYN-C02, DYN-C06, DYN-C08, DYN-C09.

Audit finding: Gauge-owner identities must map to one kinetic owner, lawful domains, quotient, and exactly the physical vector kernel; the current crosswalk omits Dynamics entirely.

Required execution:

map each gauge owner to one kinetic owner.

construct BRST/domain-reduced vector operator.

derive physical kernel and prove 8+3+1 with zero extra modes.

Claim ceiling / action: Add DYN-C09 and refresh the crosswalk; existing SG-2 evidence can populate it.

12.15 `SG-3`

Dynamics role: LOAD-BEARING. Source terminal under test: DERIVED-GIVEN-E / RESOLVED +0. Required rows: DYN-C01, DYN-C06, DYN-C08, DYN-C09.

Audit finding: The chiral index and no-mirror claim require the physical Dirac operator/domain/kernel and quantum gauge consistency, not only a topological count.

Required execution:

construct Dirac operator on exact parity/domain data.

derive chiral kernel and mirror disposition.

pass measure/anomaly handoff to AD/BND.

Claim ceiling / action: Add DYN-C09; integrate BND/AD evidence.

12.16 `SG-4`

Dynamics role: LOAD-BEARING. Source terminal under test: CLOSED / DERIVED-GIVEN-E / RESOLVED +0. Required rows: DYN-C01, DYN-C03, DYN-C06.

Audit finding: Charges and anomalies require one parent coupling, the fermion/ghost measure, Ward identities, and boundary/global anomaly closure.

Required execution:

derive charge couplings from parent terms.

include fermion/ghost measure.

evaluate Ward/anomaly consistency with BND-B.

Claim ceiling / action: Crosswalk expansion; BND-B remains decisive.

12.17 `SG-5`

Dynamics role: LOAD-BEARING. Source terminal under test: DERIVED-GIVEN-anchor / RESOLVED +0. Required rows: DYN-C01, DYN-C05, DYN-C09, DYN-C10, DYN-C11, DYN-C12.

Audit finding: EWSB cannot close from Actor identity alone: the parent interaction, solved background, mass/mixing matrices, physical scalar/vector spectrum, and positivity are required.

Required execution:

generate complete electroweak interaction graph.

solve order-parameter background.

derive vector/scalar mass and mixing spectra and positivity.

Claim ceiling / action: Genuine Dynamics improvement: C10-C12 and executable packets.

12.18 `SG-6`

Dynamics role: SUPPORTING. Source terminal under test: DERIVED-GIVEN-anchor / RESOLVED +0. Required rows: DYN-C05, DYN-C08, DYN-C09, DYN-C12, DYN-C15, DYN-C16.

Audit finding: Rigidity owns the terminal, but Dynamics must supply the full physical Hessian/operator, quantum physicality, tower scope, and refinement stability.

Required execution:

construct full mixed physical Hessian/operator.

supply positivity and causal evolution.

test tower/refinement stability before Rigidity terminal.

Claim ceiling / action: Strengthen Dynamics-to-Rigidity handoff; no replacement of RIG.

12.19 `SG-7`

Dynamics role: LOAD-BEARING. Source terminal under test: DISSOLVED-GIVEN-root / RESOLVED +0. Required rows: DYN-C01, DYN-C03, DYN-C08, DYN-C10, DYN-C16.

Audit finding: Threshold unification and proton-scale matching depend on complete interaction content, determinants, tower scope, and scheme/refinement stability.

Required execution:

enumerate threshold-relevant interactions and determinants.

run same-ruler matching.

test tower/regulator/scheme stability.

Claim ceiling / action: Add C10/C16 packet; Scale still owns ruler/matching provenance.

12.20 `SG-8`

Dynamics role: LOAD-BEARING. Source terminal under test: CLOSED / RESCUED / DISSOLVED-WRONG-RULER + DERIVED-GIVEN-13D-ACTOR / RESOLVED +0. Required rows: DYN-C01, DYN-C08, DYN-C09, DYN-C10, DYN-C11, DYN-C12, DYN-C16.

Audit finding: Flavor masses and mixings require a complete Yukawa/interaction graph, generated matrices, physical eigenstates, and same-ruler/refinement controls.

Required execution:

generate complete Yukawa/flavor graph.

derive mass and mixing matrices from solved background.

test physical eigenstates, positivity, and refinement.

Claim ceiling / action: Genuine Dynamics improvement: interaction and mass-generation execution.

12.21 `SG-9`

Dynamics role: LOAD-BEARING. Source terminal under test: DERIVED-GIVEN-anchor / RESOLVED +0. Required rows: DYN-C01, DYN-C06, DYN-C08, DYN-C10, DYN-C11, DYN-C16.

Audit finding: Proton safety is a universal statement over dangerous operators, selection rules, induced vertices, thresholds, and running.

Required execution:

generate all dangerous baryon-violating operators.

prove selection-rule/theorem-zero dispositions.

derive induced amplitudes, thresholds, and RG stability.

Claim ceiling / action: Genuine Dynamics improvement: complete dangerous-operator hypergraph and RG stability.

12.22 `UQF-10`

Dynamics role: LOAD-BEARING. Source terminal under test: RESOLVED +0 / DERIVED-GIVEN-anchor + CLOSED-NEGATIVE leg. Required rows: DYN-C01, DYN-C02, DYN-C05, DYN-C08, DYN-C09, DYN-C10, DYN-C12, DYN-C16.

Audit finding: Compactification consistency requires complete mixed operators/interactions, constraint closure, solvable background, physical spectrum, and tower/refinement control.

Required execution:

construct all mixed compactification operators and interactions.

solve background/constraint system.

test physical spectrum, positivity, and tower stability.

Claim ceiling / action: Add C09/C10/C12/C16; Rigidity/Boundary remain co-owners.

12.23 `UQF-14`

Dynamics role: LOAD-BEARING. Source terminal under test: CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C07, DYN-C08, DYN-C09, DYN-C12, DYN-C13, DYN-C15, DYN-C16, DYN-C17.

Audit finding: Above-cutoff causality requires a physical quantum channel, well-posed causal support, refinement/tail control, and regional/interface flux accounting.

Required execution:

construct physical high-energy channel.

establish causal initial-boundary evolution with TS.

track interface flux and refinement/tail scope.

Claim ceiling / action: Genuine improvement: TS-integrated causal and quantum-channel certificates.

12.24 `UQF-3`

Dynamics role: LOAD-BEARING. Source terminal under test: CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C03, DYN-C06, DYN-C08, DYN-C09, DYN-C12, DYN-C13, DYN-C15, DYN-C16.

Audit finding: Reflection positivity is not discharged by formal self-adjointness; the full physical measure, quotient, continuation, poles, and regulator/tail stability are needed.

Required execution:

derive full physical measure and operator quotient.

test reflection positivity/reconstruction and poles.

test causal/channel and regulator stability.

Claim ceiling / action: Genuine Dynamics improvement: executable positivity/continuation packet.

12.25 `UQF-4`

Dynamics role: LOAD-BEARING. Source terminal under test: CLOSED / DERIVED-GIVEN-13D-SHAPE / GLOBAL-ANOMALY-CONSISTENT / RESOLVED +0. Required rows: DYN-C03, DYN-C06.

Audit finding: Global anomalies are quantum-measure and Ward/QME obstructions; Boundary B owns local/global relative trivialization.

Required execution:

derive quantum measure/Ward residuals.

supply local/global anomaly data to Boundary B.

do not treat classical BRST closure as quantum closure.

Claim ceiling / action: Crosswalk expansion; no new Dynamics submodule.

12.26 `UQF-5A/5B`

Dynamics role: LOAD-BEARING. Source terminal under test: CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C01, DYN-C03, DYN-C07, DYN-C08, DYN-C09, DYN-C12, DYN-C15, DYN-C16.

Audit finding: A graviton sector needs the full physical operator, gauge quotient, positive poles/residues, causal evolution, and stable tower/truncation scope.

Required execution:

construct gauge-reduced graviton operator.

derive positive poles/residues and causal propagation.

test tower/truncation stability.

Claim ceiling / action: Genuine improvement: positivity and causal/refinement packets.

12.27 `UQF-5C`

Dynamics role: LOAD-BEARING. Source terminal under test: CLOSED / CERTIFIED-IRREDUCIBLE-FLOOR / RESOLVED +0. Required rows: DYN-C06, DYN-C08, DYN-C12, DYN-C15, DYN-C16.

Audit finding: A constructive UV completion requires nonperturbative/refinement evidence and quantum physicality. The existing irreducible-floor terminal only requires that finite evidence not be promoted.

Required execution:

for constructive claim, test nonperturbative/refinement stability and quantum physicality.

for irreducible-floor terminal, prove finite evidence cannot be promoted.

Claim ceiling / action: Add C16 for any constructive claim; current external-wall terminal remains honest.

12.28 `UQF-7`

Dynamics role: LOAD-BEARING. Source terminal under test: DERIVED-GIVEN-anchor / RESOLVED +0. Required rows: DYN-C03, DYN-C06, DYN-C09.

Audit finding: Anomaly descent consumes the chiral operator/domain/kernel and quantum measure, then passes to AD/BND for descent and gluing.

Required execution:

construct chiral operator/domain/kernel.

derive measure contribution.

handoff descent and gluing to AD/BND.

Claim ceiling / action: Add C09 crosswalk; integrate AD-1.

12.29 `UQF-9`

Dynamics role: LOAD-BEARING. Source terminal under test: CERTIFIED-IRREDUCIBLE / RESOLVED +0. Required rows: DYN-C01, DYN-C03, DYN-C06, DYN-C08, DYN-C09, DYN-C16.

Audit finding: Seeley–DeWitt/UV calculations require the complete operator, domain, measure, boundary terms, and strict finite-order/refinement scope.

Required execution:

construct complete heat-kernel operator/domain/measure.

calculate finite coefficients.

enforce strict finite-order and refinement scope.

Claim ceiling / action: Add C09/C16; no promotion to UV completion.

12.30 `theta-bar-QCD`

Dynamics role: LOAD-BEARING. Source terminal under test: DISSOLVED-GIVEN-root / RESOLVED +0. Required rows: DYN-C01, DYN-C05, DYN-C06, DYN-C10, DYN-C11, DYN-C14, DYN-C16.

Audit finding: A constructive strong-CP mechanism needs topological interactions, anomaly consistency, relaxation/transition dynamics, and radiative stability. A dissolution terminal may use a narrower subset.

Required execution:

generate topological and anomalous interactions.

derive relaxation/transition dynamics for constructive route.

test radiative and refinement stability or preserve narrower dissolution route.

Claim ceiling / action: Add C10/C11/C14/C16 for constructive leg; preserve scoped dissolution route.

13. Cross-block handoff matrix

| Interface | Dynamics consumes | Dynamics emits | Firewall | |---|---|---|---|

14. Dynamics residual vector and closure condition

Define \[\mathcal R{\mathrm{DYN}}=(r1,\ldots,r_{19}).\]

r_1: count or quantified norm of unowned parent terms.

r_2: count or quantified norm of undisposed variables/equations.

r_3: count or quantified norm of unclosed constraints/rank strata.

r_4: count or quantified norm of omitted determinant/measure terms.

r_5: count or quantified norm of unsolved background/reaction equations.

r_6: count or quantified norm of Ward/anomaly/domain residuals.

r_7: count or quantified norm of incorrect ordinary-source response.

r_8: count or quantified norm of scope/tail residuals.

r_9: count or quantified norm of unclassified operators/modes.

r_10: count or quantified norm of undisposed interaction edges.

r_11: count or quantified norm of unowned masses/mixings/transitions.

r_12: count or quantified norm of negative/complex physical-mode residuals.

r_13: count or quantified norm of invalid quantum channels/instruments.

r_14: count or quantified norm of unresolved history variables/intervals.

r_15: count or quantified norm of ill-posed causal data/domains.

r_16: count or quantified norm of unstable regulator/refinement directions.

r_17: count or quantified norm of unbalanced regional/interface currents.

r_18: count or quantified norm of failed destructive controls.

r_19: count or quantified norm of stale or missing authority/evidence hashes.

A Dynamics-supported positive terminal requires every hard applicable residual to vanish and every claimed global remainder to satisfy its bound. A negative terminal requires a reproducible failed hard constraint. An external-wall terminal requires proof that the gate demands evidence outside the current executable/known class, together with exact reopen conditions. Missing evidence is OPEN, not zero.

15. Machine validator logic

def adjudicate_dynamics(gate, selected_rows, evidence, residuals, controls):
    assert gate.authority_hashes_are_frozen
    for row in selected_rows:
        if row not in evidence:
            return "OPEN", f"missing {row}"
        if evidence[row].status == "NOT-APPLICABLE" and not evidence[row].type_proof:
            return "FAIL", f"unproved N/A for {row}"
        if evidence[row].status == "FAIL":
            return "FAIL", row
        if evidence[row].status != "PASS":
            return "OPEN", row
    if any(c.status != "PASS" for c in controls):
        return "FAIL", "destructive control"
    if residuals.any_hard_nonzero():
        return "OPEN", "nonzero residual"
    if gate.claim_is_global and not evidence["DYN-C08"].tail_theorem:
        return "OPEN", "scope promotion"
    return "DYNAMICS-SUFFICIENT", gate.scope_ceiling

The validator does not declare the full gate terminal. It emits a Dynamics adjudication consumed by the cross-block status engine.

16. Required evidence tree

<GATE>/DYNAMICS/
  00_CONTRACT/
    GATE_CONTRACT.yaml
    AUTHORITY_HASHES.json
    DYNAMICS_ROW_SELECTION.json
  01_PARENT_LAW/
    PARENT_ACTION_MANIFEST.yaml
    PRIMITIVE_TERM_LEDGER.csv
    VARIATIONAL_DISPOSITION.csv
  02_CONSTRAINT_MEASURE_BACKGROUND/
    EQUATION_LEDGER.csv
    CONSTRAINT_CLOSURE.json
    PHYSICAL_MEASURE.json
    BACKGROUND_SOLVABILITY.json
  03_OPERATORS/
    PHYSICAL_OPERATOR_PACKETS/
    MIXED_BLOCK_LEDGER.csv
    OPERATOR_SATURATION.json
  04_INTERACTIONS_TRANSITIONS/
    INTERACTION_HYPERGRAPH.json
    DANGEROUS_OPERATOR_LEDGER.csv
    MASS_MIXING_TRANSITION.json
  05_QUANTUM_HISTORY_CAUSAL/
    QUANTUM_PHYSICALITY.json
    QUANTUM_CHANNEL.json
    NONEQUILIBRIUM_HISTORY.json
    CAUSAL_IBVP.json
  06_REFINEMENT_FLUX/
    RG_REFINEMENT.json
    REGIONAL_FLUX.json
  07_CONTROLS/
    DESTRUCTIVE_CONTROLS.json
  08_ADJUDICATION/
    DYNAMICS_ROW_STATES.csv
    DYNAMICS_RESIDUAL_VECTOR.json
    DYNAMICS_ADJUDICATION.md
    SHA256SUMS.txt

17. Status grammar, terminals, and anti-promotion rules

PASS, FAIL, OPEN, NOT-EVALUATED, NOT-APPLICABLE, CONSTRUCTION-ANCHOR, CONDITIONAL-ON-BND-A, CONDITIONAL-ON-BND-B, and RESTART-REQUIRED retain their package meanings.

An action is not a solved background.

An equation list is not a well-posed evolution.

A declared Actor is not a derived physical kernel.

A free spectrum is not an interaction theory.

A fitted matrix is not a parent-derived mass matrix.

Formal self-adjointness is not physical positivity.

Trace preservation is not a physical open-system channel.

A static identity is not a cosmological history.

Local conservation is not regional closure.

One truncation or regulator is not a continuum/UV theorem.

A zero-mode result is not a full-tower result.

An integrated anomaly cancellation is not local or global boundary closure.

18. Reopen conditions

a new Stage support, Actor, Rulebook rule, boundary stratum, or variational owner appears.

a new invariant parent term or interaction edge survives the grammar.

a constraint rank, gauge complex, or physical measure changes.

a new physical pole, zero mode, mirror, edge mode, or mixed block appears.

a claimed theorem-zero interaction is generated radiatively.

a mass/mixing/transition changes under lawful normalization or matching.

positivity, channel, causal, history, refinement, or flux controls fail.

a gate produces a Dynamics distinction not representable by DYN-C01–DYN-C17.

authority hashes or upstream branch objects change.

18A. Legacy-preservation theorem and revision discipline

V4.2 is valid as a successor only if all of the following hold:

Source retention: the exact BB-DYN-3.3.1 source is present and hash-verified.
Section mapping: every substantive old section maps to an explicit V4.2 section or preserved clause.
Witness monotonicity: no old required witness is replaced by a weaker witness.
Failure monotonicity: every old fail trigger remains capable of producing FAIL or OPEN.
Control monotonicity: every old destructive control remains executable.
Status compatibility: all old status states retain their meanings.
Claim-ceiling monotonicity: no local, zero-mode, finite-tower, boundary-incomplete, or construction-anchor result is promoted by the revision.
Correction transparency: source defects are corrected only through an explicit correction ledger.
Gate regression: SG-2, SG-5, UQF-3, BG-10, and UQF-14 must be rerun target-blind before canonical ratification.
Hostile review: an independent review must attempt to find omitted terms, equations, determinants, interactions, domains, histories, regulators, and fluxes.

Define the preservation residual

\[ \mathcal R{\mathrm{pres}}=(N{\mathrm{unmapped\ legacy\ clauses}},N{\mathrm{weakened\ witnesses}},N{\mathrm{lost\ fail\ triggers}},N{\mathrm{lost\ controls}},N{\mathrm{uncorrected\ source\ defects}},N_{\mathrm{hash\ mismatches}}). \]

A V4.2 package-level preservation pass requires

\[ \boxed{\mathcal R_{\mathrm{pres}}=0.} \]

This package satisfies the documentation-level preservation test. Gate-level physical sufficiency remains subject to execution.

19. Authority and claim ceiling

This is a development authority candidate. It is more complete than V4.0 as a standalone execution object, but it does not ratify itself and does not convert prior gate evidence into PASS. Ratification requires hostile review, schema/validator testing, target-blind calibration on SG-2, interaction calibration on SG-5, positivity calibration on UQF-3, nonequilibrium calibration on BG-10, and causal/interface calibration on UQF-14. Any failed calibration repairs the reusable row and propagates to all mapped gates.

Appendix A — Constraint registry

| ID | Witness | Minimal discharge | Fail trigger | |---|---|---|---|

| DYN-C01 | Parent-action manifest and term provenance | Every primitive term and gauge connection has one lawful owner, support, coefficient provenance, symmetry, derivative order, boundary status, and microscopic/effective scope. | Unowned terms, double-counted aliases, or a gauge owner without a parent-action term. |

| DYN-C02 | Dirac–Bergmann or BV–BFV closure | All constraints, ranks, brackets, residual gauges, boundary terms, and physical degree counts are computed to closure on the claimed stratum. | Early termination, rank change, omitted boundary constraint, or unresolved residual gauge. |

| DYN-C03 | Physical measure and determinant derivation | All FP/Dirac/BV determinants and field dependence are retained in loops, matching, and stress calculations. | A determinant is dropped as a constant without proof. |

| DYN-C04 | Full metric variation and stress | Stress is derived from the complete action and measure, including constraints, boundaries, ghosts, and solved multiplier dependence. | No-work or absence from a propagator is substituted for zero stress. |

| DYN-C05 | Retained-plus-reaction solvability | The complete coupled equations have a solution with full-rank Jacobian or an existence theorem on the declared domain. | Normal forces lie outside multiplier span or retained equations are unsolved. |

| DYN-C06 | Ward/BV identity and global boundary multiplier closure | The domain is preserved, anomalies cancel, and multiplier/boundary equations admit a global solution. | Unresolved Ward identity, anomaly, boundary equation, or QME residual. |

| DYN-C07 | Physical response, conservation, and ordinary-source control | Localized and nonconstant sources yield the correct conserved causal response while protected constants follow VAC. | Ordinary matter is degravitated, conservation fails, or response is acausal. |

| DYN-C08 | Scope theorem or bounded truncation report | The result declares zero-mode, finite-tower, EFT, or all-mode scope, with a tail theorem for global claims. | A local or finite result is promoted beyond scope. |

| DYN-C09 | Operator construction and physical kernel/spectrum certificate | Linearize the complete parent equations, build the gauge-fixed and constraint-reduced operators on the lawful domains, and publish kernels, zero modes, spectra, response functions, multiplicities, and unresolved tails. | A gate uses a declared Actor or expected spectrum without deriving the corresponding physical operator/kernel, or omits a mixed/operator block. |

| DYN-C10 | Complete interaction and source hypergraph | Enumerate every parent-owned interaction vertex, source edge, representation contraction, selection rule, theorem-zero edge, dangerous operator, support, scale, and boundary domain. | A coupling, decay, portal, Yukawa, CP source, or dangerous operator is inserted or omitted without a complete parent-law disposition. |

| DYN-C11 | Mass, mixing, transition, and decay derivation | Mass matrices, mixings, symmetry breaking, decay widths, threshold transitions, and effective vertices are derived from C10 plus the solved background and are diagonalized/matched with stated scope. | A matrix or transition is supplied by hand, the background does not solve the parent equations, or physical eigenstates/widths are not derived. |

| DYN-C12 | Quantum physicality, positivity, and analytic-continuation certificate | After gauge/BRST quotient, establish a positive physical pairing or reflection-positivity/equivalent reconstruction, pole and residue signs, continuation prescription, and absence/disposition of negative-norm states. | Formal self-adjointness, Euclidean convergence, or BRST nilpotency is used without a physical positivity/pole certificate. |

| DYN-C13 | Closed/open quantum evolution and probability instrument | Closed sectors have unitary normalized evolution; open sectors publish a completely positive trace-preserving channel or justified instrument, environment, exchange currents, approximation bound, and Observer handoff. | A trace-preserving but nonphysical map, unnormalized probability rule, undeclared environment, or hidden information loss is used. |

| DYN-C14 | Nonequilibrium, thermal, and cosmological-history evolution | Publish initial state, thermal/kinetic/transport equations, entropy and charge production, phase-transition dynamics, production/washout/freeze-out, perturbations, and uncertainty through the claimed history. | A static potential or constant-shift result is promoted to a finite-time cosmological, baryogenesis, dark-matter, or transition claim. |

| DYN-C15 | Well-posed causal initial-boundary-value problem | Prove or compute hyperbolicity/evolution well-posedness, constraint propagation, boundary compatibility, causal support, stability under allowed data, and synchronization/Observer handoffs. | Equations exist but evolution is nonunique, unstable, superluminal outside the declared cone, domain-incompatible, or not globally composable. |

| DYN-C16 | RG, refinement, regulator, and truncation stability | Use nested operator bases/resolutions and admissible regulator/scheme families; track generated operators, fixed points/flows, critical data, convergence, matching, and omitted-tail bounds. | A result exists only in one truncation, basis, regulator, or scheme and changes materially under lawful refinement. |

| DYN-C17 | Regional, horizon, interface, and information-flux balance | For regions separated by boundaries, defects, horizons, or cuts, publish charge/energy/probability/information currents, gluing law, edge terms, exchange channel, and finite Observer records. | Local conservation is claimed while flux through an interface is omitted, or subsystem nonunitarity is mistaken for global loss without a channel ledger. |

Appendix B — Gate-to-row crosswalk

| Gate | Role | Dynamics rows | Source terminal under test | |---|---|---|---|

Appendix C — Standalone execution prompt

Read this authority and the frozen gate inputs. Execute only the Dynamics rows selected for the gate. Do not load the expected numerical answer until after calculation. Generate the complete parent-term, equation, constraint, physical-operator, interaction, transition, quantum/history/causal, refinement, and regional slices required by type. Freeze all failures before repair. A repair must be reusable across every gate invoking the affected row. Run every destructive control, compute the Dynamics residual vector, and report physical result, Dynamics sufficiency, project dependency, claim ceiling, evidence hashes, and exact reopen triggers separately. Never convert missing evidence into zero, a finite result into a global result, or a declared Actor/interaction into a derived one.

Appendix D — Exact archival BB-DYN-3.3.1 source

The following archival annex is byte-identical to the source file whose SHA-256 is f3ad4b47e7726a05128333a469c43d5e571877ce7aab5ecd5b1fadf96756847e. It is included for mechanical preservation review. The operative V4.2 clauses are the main-body sections above; the annex prevents silent historical loss.

---
title: "BB-DYN-3.3.1 — Parent Dynamics, Constraints, Gauge Ownership, Background, Boundary Anomaly, and Response"
building_block_id: "BB-DYN-3.3.1"
version: "3.3.1"
date: "2026-07-24"
status: "DEVELOPMENT AUTHORITY — SHP-C09 GAUGE-OWNER INTERFACE MERGED — NOT FROZEN"
scope: "Complete owned specification under package v3.3.2"
protocol_freeze: false
canonical_ratification: false
package_authority_version: "3.3.2"
---

# BB-DYN-3.3.1 — Parent Dynamics, Constraints, Gauge Ownership, Background, Boundary Anomaly, and Response

## 0. Purpose

Dynamics answers:

> **Which lawful changes occur on the complete Shape, which equations define its backgrounds, how exact constraints are preserved, how quantum corrections modify the equations, and how the system responds separately to vacuum offsets and ordinary excitations?**

This block prohibits four substitutions:

\[
\text{kinematic permission}\neq\text{nonzero amplitude},
\]

\[
\text{constraint no-work}\neq\text{zero stress},
\]

\[
\text{no propagator}\neq\text{radiative solvability},
\]

\[
\text{internal reaction solvable}\neq\text{vacuum energy degravitated}.
\]

## 1. Parent action

Every candidate must supply a typed parent action or an explicitly scoped non-action replacement.

A general action ledger is

\[
S_{
m parent}=S_{
m grav}+S_{
m gauge}+S_{
m matter}+S_{
m scalar}
+S_{
m boundary}+S_{
m constraint}+S_{
m global}+S_{
m domain}.
\]

For every term publish:

- support and dimensionality;
- field owner;
- derivative order;
- exact and broken symmetries;
- coefficient provenance;
- boundary variation;
- whether microscopic, structural, global, or matching-only;
- stress-energy contribution;
- vacuum-energy contribution;
- cutoff and scheme scope.

An arbitrary dense kernel entry without a parent-law owner is prohibited.

## 2. Complete equation vector

Let the independent variables be

\[
z^I=(g_{\mu\nu},\gamma_{mn},g_{\mu m},A_M,\Psi,\phi,b,\lambda,\sigma,\ldots).
\]

The complete background and fluctuation equations are

\[
\mathcal F_I[z]\equiv\frac{\delta\Gamma}{\delta z^I}=0,
\]

supplemented by boundary, global, gauge, and constraint equations.

The candidate must publish an equation ledger:

equation: equationid: variedobject: localorglobal: bulkorboundary: differentialoralgebraic: independentafteridentities: sourceterms: constraintcouplings: observerprojection: solutionstatus:


### 2.1 Equation counting

Before claiming a background solution:

1. count independent unknown functions and global variables;
2. count independent equations after Noether and Bianchi identities;
3. classify gauge freedoms;
4. classify second-class constraints;
5. include boundary and junction equations;
6. verify rank on the claimed stratum;
7. prove or compute existence of a solution.

A visually plausible product ansatz is not a solution certificate.

## 3. Constraint classification and closure

Constraints are typed as:

- first-class gauge constraints;
- second-class physical constraints;
- constitutive restrictions;
- boundary/gluing constraints;
- global constraints;
- effective matching relations.

For Hamiltonian variables, the total Hamiltonian is

\[
H_T=H_0+u^A\Xi_A.
\]

The Dirac–Bergmann algorithm must:

1. list primary constraints;
2. impose preservation \(\dot\Xi_A\approx0\);
3. generate every secondary and higher constraint;
4. terminate with constant rank on the claimed stratum;
5. classify first- and second-class sectors;
6. determine multipliers and residual gauge functions;
7. verify boundary compatibility;
8. compute the physical degree-of-freedom count.

For second-class constraints,

\[
C_{AB}=\{\Xi_A,\Xi_B\}
\]

must be invertible on the physical stratum and

\[
\{F,G\}_D=\{F,G\}-\{F,\Xi_A\}(C^{-1})^{AB}\{\Xi_B,G\}.
\]

Rank change is a branch change or singular stratum, not a small correction.

## 4. Physical measure

For a second-class system,

\[
D\mu_{
m phys}=D\mu_0\prod_A\delta(\Xi_A)\sqrt{\det C}.
\]

The determinant must be included in effective actions, matching, and stress calculations.

If \(C\) depends on retained fields,

\[
\Delta\Gamma_C=-\frac{i}{2}\operatorname{Tr}\log C
\]

or the appropriate Euclidean counterpart contributes physical terms.

A field-dependent determinant cannot be dismissed as normalization.

## 5. No-work and stress are separate

For ideal constraints,

\[
\lambda^A d\Phi_A=0
\]

along admissible displacements.

This proves no virtual work in constrained directions. It does not establish zero stress-energy.

For

\[
S_{\rm constraint}=\int d^Dx\sqrt{-g}\,\lambda^A\Phi_A,
\]

\[
T^{\rm constraint}_{MN}
=-\frac{2}{\sqrt{-g}}\frac{\delta S_{\rm constraint}}{\delta g^{MN}}.
\]

The calculation must include:

- metric variation of the volume form;
- explicit metric dependence of \(\Phi_A\);
- metric dependence of multipliers when induced by solved equations;
- determinant and ghost terms;
- boundary contributions.

Zero constraint stress is a result with conditions, not a default property.

## 6. Constrained reaction equations

For retained variables \(q^a\), constrained variables \(\phi^r\), and constraints \(\Phi_\alpha(q,\phi)=0\), the renormalized equations are

\[
\frac{\delta\Gamma_0}{\delta q^a}
+\lambda^\alpha\frac{\delta\Phi_\alpha}{\delta q^a}=0,
\]

\[
\frac{\delta\Gamma_0}{\delta\phi^r}
+\lambda^\alpha\frac{\delta\Phi_\alpha}{\delta\phi^r}=0,
\]

\[
\Phi_\alpha=0.
\]

### 6.1 Block-separable case

If

\[
\frac{\delta\Phi_\alpha}{\delta q^a}=0
\]

and the normal Jacobian

\[
N_{\alpha r}=\frac{\delta\Phi_\alpha}{\delta\phi^r}
\]

has full rank, the normal equations determine reactions when

\[
-\left.\frac{\delta\Gamma_0}{\delta\phi^r}\right|_{\Phi=0}
\in\operatorname{im}N^T.
\]

This prevents normal-force overdetermination only under that span condition.

### 6.2 General case

If constraints depend on retained variables, multipliers modify retained equations. The full coupled system must be solved.

### 6.3 Global solvability

Pointwise algebra is insufficient. The multiplier system must satisfy:

- regularity;
- boundary and fixed-set parity;
- junction conditions;
- global integrability;
- Ward identities;
- anomaly cancellation;
- conserved-charge balance.

## 7. Background-equation completeness

A candidate background receives one of four Dynamics statuses:

### 7.1 Parent solution

Every varied parent equation and boundary equation is satisfied.

### 7.2 Constrained reaction solution

Displaced equations are replaced by a complete, solvable reaction system, including stress and boundary effects.

### 7.3 Effective external background

The Stage is externally supplied. The reduced theory may be useful, but it does not derive the background as a parent vacuum.

### 7.4 Inconsistent background

The complete equation system has no solution at the claimed object.

A closure statement must name which status is used.

## 8. Radiative solvability

Let \(\Gamma_k\) be the effective action at scale \(k\). Radiative consistency requires more than preservation of the classical constraint surface.

At each claimed order or Wilsonian step, test:

- closure of the corrected constraint algebra;
- rank stability;
- normal-force span;
- retained equation solvability;
- boundary compatibility;
- anomaly and Ward identities;
- generation of forbidden operators;
- determinant contributions;
- parameter and counterterm provenance.

A forbidden mode need not be regenerated for the theory to fail. Equations with no solution are a separate failure.

## 9. Physical stability interface

Dynamics supplies the effective Hessian to `BB-RIG-1.1`.

After gauge quotient and exact constraints,

\[
Q_{\rm phys}=P_{\rm phys}^{T}\,\delta^2\Gamma\,P_{\rm phys}.
\]

The supplied packet must include:

- kinetic metric;
- gauge fixing and ghosts;
- mixed blocks;
- boundary domain;
- scale and scheme;
- zero modes;
- negative modes;
- intended protected scalars;
- tower scope;
- uncertainty.

Dynamics may not label an isolated critical point stable without the physical Hessian result.

## 10. Vacuum-offset response interface

A field-independent shift of a protected matter sector is

\[
\mathcal L_m\rightarrow\mathcal L_m-c.
\]

Dynamics must expose how it enters the complete equations.

For ordinary Einstein coupling, the external equation shifts by a term proportional to

\[
c\,g_{\mu\nu}.
\]

Constraint reactions in internal directions do not automatically remove this external response.

The vacuum-response packet sent to `BB-VAC-1.1` contains:

vacuumresponsepacket: protectedsector: constantshiftparameter: externalmetricequation: internalequations: constraintreactionequations: globalauxiliaryequations: boundaryequations: determinantterms: matchingterms: gravitonloopscope: ordinarystressresponse: solvedresponse_operator:


## 11. Ordinary-gravity control

Any vacuum-offset mechanism must preserve lawful response to nonconstant stress.

The negative control is:

- add a constant \(-c\) to the protected Lagrangian;
- verify local curvature observables do not change in the protected scope;
- add a localized excitation with nontrivial traceless or gradient stress;
- verify ordinary gravitational response remains.

A mechanism that removes all stress from the gravitational equations fails.

## 12. Constant shifts versus phase transitions

A constant threshold correction and a finite-time phase transition are distinct.

Dynamics must classify:

- static additive shift;
- changing condensate;
- latent heat;
- radiation production;
- nonadiabatic boundary or global response;
- historical averages;
- residual present value.

A constant-shift identity does not automatically solve cosmological transition history.

## 13. Probability, causality, and conservation

For closed quantum sectors, the generator must be self-adjoint on the physical domain or possess an equivalent unitary kernel.

For open sectors, declare:

- environment;
- channel;
- normalization;
- exchange currents;
- observer access;
- approximation bound.

The law must preserve, at the claimed scope:

- probability;
- gauge and BRST constraints;
- exact charges;
- boundary flux balance;
- causal support;
- operational no-signalling.

## 14. Dynamics certificate

dynamicscertificatev3: candidateid: branchid: parentaction: primitivetermledger: completeequationvector: equationcountandidentities: constrainttypes: diracbergmannclosure: rankstrata: physicalmeasure: determinantcontributions: constraintstress: multiplierboundaryproblem: backgroundstatus: backgroundsolution: radiativesolvability: wardidentities: anomalyresult: physicalhessianpacket: vacuumresponsepacket: ordinarygravitycontrol: phasetransitionscope: fulltowerscope: evidence_hashes: verdict:


## 15. Negative controls

### 15.1 No propagator but no solution

Remove a deformation field from the propagator but choose a radiative normal force outside the multiplier span.

Expected result: `FAIL / RADIATIVE OVERDETERMINATION`.

### 15.2 Constraint no-work with nonzero stress

Use a metric-dependent constraint that does no virtual work along admissible motion.

Expected result: no-work passes, stress-zero claim fails.

### 15.3 Vacuum degravitation that also removes matter gravity

Project out every trace and traceless source indiscriminately.

Expected result: vacuum shift passes, ordinary-gravity control fails.

### 15.4 Frozen Stage with abandoned internal equations

Do not vary the internal metric and supply no reaction or background equation.

Expected result: `EFFECTIVE EXTERNAL BACKGROUND`, not parent solution.

## 16. Falsifiers and reopen triggers

This block fails or reopens if:

- the parent action is incomplete;
- a primitive move lacks an owner;
- equation counting omits a boundary or global equation;
- Dirac closure or rank is incomplete;
- determinant terms are omitted;
- no-work is used as a stress proof;
- no-propagator is used as a solvability proof;
- a background is called a solution without all equations;
- a constant vacuum shift changes local curvature in the claimed protected scope;
- ordinary nonconstant stress fails to gravitate;
- a phase-transition claim is inferred from constant-shift cancellation;
- a zero-mode result is promoted to the full tower.

## 17. Terminal

BB-DYN-3.3.1

DELIVERS: Parent law, complete equations, constraint and measure closure, background solvability, stress accounting, radiative response, and interfaces to rigidity and vacuum protection.

STATUS: DEVELOPMENT AUTHORITY CANDIDATE — NOT FROZEN.


## Integrated boundary/orbifold authority

This block is part of the **Candidate-Neutral Building-Block Authority v3.1 — Boundary and Inflow Development Candidate**.

The following rule is binding across the set:

> A bulk or quotient-space anomaly cancellation statement does not close a theory with orbifold fixed sets or physical boundaries. Each stratum requires a local anomaly ledger, and the complete quantum theory requires a relative/global trivialization compatible with gluing.

The dedicated owner is `BB-BND-1 — Orbifold Fixed-Set, Relative-Anomaly, and Inflow Completion`.

Every candidate containing a boundary, fixed set, defect, quotient singularity, interface, or parity projection must provide a `boundary_anomaly_completion_certificate`. Until that certificate passes:

- a chirality or no-mirror result is **CONDITIONAL-ON-BND**;
- quantum BRST/BV nilpotency is **CONDITIONAL-ON-BND**;
- a global-bordism result for the closed bulk target is not a complete boundary result;
- cancellation after integrating over the compact direction is not accepted as local gauge invariance;
- no gate may claim that the interval/orbifold construction is fully quantum consistent.

## Boundary/orbifold completion — stratified quantum gauge consistency

### 1. Complete gauge variation

For a \(d+1\)-dimensional parent with \(d\)-dimensional fixed sets \(F_a\), the renormalized gauge variation is decomposed as

\[
\delta_\epsilon\Gamma_{\rm tot}
=
\delta_\epsilon\Gamma_{\rm bulk}
+
\sum_a
\delta_\epsilon\Gamma_{F_a}
+
\delta_\epsilon S_{\rm inflow}
+
\delta_\epsilon S_{\rm ct}.
\]

For four-dimensional fixed sets, write the descent data

\[
I_6=dI_5^{(0)},
\qquad
\delta_\epsilon I_5^{(0)}=dI_4^{(1)}(\epsilon,A).
\]

A bulk inflow action of the form

\[
S_{\rm inflow}
=
2\pi i\,k\int_{Y_5}I_5^{(0)}
\]

has boundary variation

\[
\delta_\epsilon S_{\rm inflow}
=
2\pi i\,k
\sum_a s_a
\int_{F_a}I_4^{(1)},
\]

where \(s_a\) is fixed by the outward-normal orientation. The coefficient \(k\) must satisfy the appropriate quantization and global-form conditions.

### 2. Fixed-set local equations

For each fixed set define

\[
\mathcal A_a^{(1)}
=
\mathcal A_{a,\rm projected\ bulk}^{(1)}
+
\mathcal A_{a,\rm localized}^{(1)}
+
\mathcal A_{a,\rm measure}^{(1)}
+
\mathcal A_{a,\rm counterterm}^{(1)}
+
\mathcal A_{a,\rm inflow}^{(1)}.
\]

The local pass condition is

\[
\boxed{\mathcal A_a^{(1)}=0\quad\text{for every }a}
\]

as a cohomology class under all allowed gauge transformations.

The weaker condition

\[
\sum_a\mathcal A_a^{(1)}=0
\]

is only an integrated check. It does not prove local gauge invariance.

### 3. Quantum master equation with boundaries

The candidate must formulate the quantum gauge system using BV–BFV or an equivalent boundary-complete formalism.

Schematically,

\[
\frac12(S,S)-i\hbar\Delta S
=
\pi^*S_{\partial}
\]

before boundary completion. Full closure requires a compatible boundary state/functional and counterterm/inflow system such that the total quantum master equation is satisfied.

A bulk statement \(Q_{\rm BRST}^2=0\) is insufficient when the measure has fixed-set support.

### 4. Consistent versus covariant anomalies

The ledger must state whether it uses:

- consistent anomalies;
- covariant anomalies;
- Bardeen–Zumino shifted currents.

All fixed-set and inflow entries must use one compatible convention. A Bardeen–Zumino polynomial may redistribute anomaly between currents or strata, but it cannot remove the total anomaly class.

### 5. Regulator and parity dependence

Localized anomalies can depend on the parity/domain assignment and on how bulk fermions are regulated. The final anomaly class must be regulator-independent after allowed local counterterms are included.

The certificate must report:

- regulator;
- consistent-current convention;
- parity signs;
- fixed-set weights;
- localized spectrum;
- allowed counterterms;
- invariant remainder.

### 6. Global relative anomaly equation

Perturbative cancellation is not enough. The exponentiated fermion determinant is a section of an anomaly/determinant line.

The complete parent-plus-boundary system must provide a gluing-compatible trivialization:

\[
Z_{\rm boundary}\,
Z_{\rm inflow}
\in\mathbb C
\]

rather than an untrivialized line.

For every closed test obtained by gluing or forming a mapping torus, require

\[
\exp\!\left(2\pi i\,\frac{\eta+h}{2}\right)
\,
\exp(2\pi i S_{\rm top})
=
1
\]

in the declared convention and tangential structure.

### 7. Dynamics certificate additions

boundaryquantumdynamics: fixedsetids: allowedgaugetransformations: anomalyconvention: consistent|covariant regulator: bulkanomalypolynomial: projectedbulkcontributionsbyfixedset: localizedfieldcontributions: measureandghostcontributions: counterterms: inflowaction: inflowcoefficientquantization: orientationsigns: localresiduals: bvbfvorequivalentcompletion: determinantline: relativeetaorbordismtest: gluingtest: quantummasterequationresult: evidencehashes: verdict:


### 8. New Dynamics falsifiers

Dynamics fails if:

- only the integrated anomaly is zero;
- an inflow coefficient is selected after reading the residual;
- the coefficient is not globally quantized;
- a boundary condition is not compatible with the Dirac/gauge operator domain;
- the local anomaly convention changes between rows;
- the determinant line remains untrivialized;
- the BV quantum master equation is asserted from classical Jacobi closure alone.

# Block-Specific Standalone Interface — Dynamics

## Owned questions

This block alone owns:

- the typed parent action;
- the complete equation vector;
- constraint classification and preservation;
- physical measure and determinant ownership;
- stress of multiplier, boundary, and constraint sectors;
- retained/reaction-equation solvability;
- Ward identities and BV/BFV quantum consistency;
- ordinary probability, causality, conservation, and nonconstant-stress response.

## Required inputs

- complete Shape and boundary manifests;
- constraint and permission packets;
- Scale/scheme packet;
- complete field and Actor inventory;
- candidate-specific parent terms.

## Required outputs

- parent-action manifest;
- complete Euler–Lagrange and constraint-equation ledger;
- Dirac/BV/BFV closure;
- physical measure;
- stress and reaction calculations;
- background classification;
- radiative-solvability result;
- Ward/anomaly interface;
- Dynamics certificate.

## Non-ownership boundary

Dynamics does not by itself prove:

- candidate uniqueness;
- intrinsic rigidity;
- full physical stability without the Rigidity block;
- vacuum-offset protection without the Vacuum block;
- local/global fixed-set anomaly closure without the Boundary block.

## Observer-response handoff

Dynamics supplies the physical evolution, conserved currents, response functions, and physical measure consumed by OBS. OBS cannot repair an inconsistent Dynamics by projection. Conversely, a lawful parent response cannot be compared with data until OBS has produced the correct record functional.

For time-dependent vacuum tests, Dynamics must evolve the protecting sector and supply the constraint-algebra history required by `VAC-C11`.

## Gauge-owner and kinetic-term consistency

Dynamics consumes the `SHP-C09` gauge-owner ledger.

For every surviving generator \(T_A\), the parent action must identify exactly one independent connection variable and one owning kinetic structure. Metric Kaluza–Klein notation and principal-bundle notation may describe one field, but the action must not count both as independent unless a second gauge sector is physically intended and appears in the spectrum.

Required checks:

1. map every gauge-owner ID to a parent-action field;
2. count independent kinetic operators;
3. count first-class gauge parameters;
4. count four-dimensional vector zero modes;
5. verify equality of these counts after constraints and quotienting;
6. verify that center/global-lift data is compatible with every charged Actor;
7. run the duplicate-owner control by treating aliases as independent and confirm that the spectrum gains an extra gauge sector.

A gauge owner with no parent-action term fails Dynamics. A parent-action connection with no Shape owner fails the one-parent audit.

## Owned hard constraints and acceptance evidence

The full controlling registry is `EVIDENCE_DISCHARGE_REGISTRY_V3_3_2.md`. The rows below are embedded because this block owns or directly co-owns them.

| ID | Required witness | Minimal discharge | Fail trigger |
|---|---|---|---|
| `GEN-C03` | Variational-ownership ledger + equation-disposition table | Every variable is marked varied, gauge, constrained, auxiliary, measured, matching, or external, with the displaced Euler–Lagrange equation explicitly retained, replaced, proved redundant, or abandoned. | A non-varied variable has no lawful equation disposition. |
| `DYN-C01` | Parent-action manifest + term provenance table | Every primitive term has an owner, support, coefficient provenance, derivative order, symmetry, boundary status, and microscopic/effective label; every gauge connection references exactly one `SHP-C09` owner ID. | A matrix element, potential, counterterm, or gauge connection has no parent-action owner, or an owner alias is independently double-counted. |
| `DYN-C02` | Dirac–Bergmann or BV–BFV closure calculation | All primary/secondary constraints, ranks, brackets, boundary terms, and residual gauges are computed until closure; the rank is constant on the claimed stratum. | The algorithm stops early, the rank changes, or boundary constraints are omitted. |
| `DYN-C03` | Physical-measure derivation + determinant artifact | The reduced measure includes all Faddeev–Popov/Dirac/BV determinants, and field dependence is retained in loops and matching. | A determinant is dropped as a constant without proof. |
| `DYN-C04` | Metric variation of all constraint/boundary sectors | The stress tensor is obtained by varying the full action and measure; the result is evaluated on the physical branch. | No-work is used as a substitute for zero stress. |
| `DYN-C05` | Solvability/Jacobian certificate | The full retained-plus-reaction equation system has a solution and a full-rank Jacobian or a theorem establishes existence in the declared domain. | Radiative normal forces lie outside the multiplier span or the retained equations have no solution. |
| `DYN-C06` | Ward/BV identity + boundary multiplier ledger | Allowed transformations preserve the domain, all measure anomalies cancel, and multiplier boundary conditions admit a global solution. | A Ward identity, anomaly, or boundary multiplier equation remains unresolved. |
| `DYN-C07` | Response-function calculation | Localized and nonconstant stress sources produce the correct causal/conservation response while protected constants are handled according to VAC. | The mechanism removes ordinary matter gravity, violates conservation, or produces acausal record response. |
| `DYN-C08` | Scope theorem or bounded truncation report | The certificate states exactly whether it covers zero modes, a cutoff tower, or all modes, with a tail theorem where a global claim is made. | A local, zero-mode, finite-EFT, or invariant-sector result is promoted beyond scope. |
| `VAC-C01` | Complete background-equation vector + equation-count/Jacobian report | External, internal, matter, boundary, constraint, and global equations are listed and solved or lawfully replaced; unknown/equation counts and rank are published. | An internal Einstein or boundary equation disappears when a Stage variable is frozen. |
| `VAC-C04` | Finite constant-shift response experiment | For each protected sector, the full equations are re-solved after \(\mathcal L_s	o\mathcal L_s-c_s\), and the curvature-record derivative or finite difference is published. | Only an infinitesimal or tree-level shift is tested while auxiliary/global response is held fixed. |
| `VAC-C06` | Localized-source negative control | Dust, radiation, pressure gradients, and localized stress still source the correct gravitational response. | The protection mechanism degravitates ordinary matter or radiation. |
| `BND-C03` | Operator-domain certificate | Dirac, gauge, ghost, scalar, and load-bearing graviton domains are self-adjoint/elliptic as required and preserved by gauge/BRST transformations. | A parity table is supplied without a lawful operator domain. |
| `BND-C07` | Boundary BV/BFV quantum-master-equation output | Ghost, measure, boundary state, and inflow contributions satisfy the relative QME and compose under gluing. | Classical BRST closure is used while the measure/domain anomaly remains. |
| `VAC-C11` | Time-dependent constraint-algebra and cosmology simulation/theorem | A time-dependent vacuum shift \(c(t)\) representing QCD/electroweak transitions is inserted; the constraint algebra remains consistent and the Friedmann/perturbation history stays within frozen bounds, or the regime is explicitly excluded with quantified lost predictions. | The mechanism passes static shifts but becomes singular, acausal, or observationally unacceptable during a finite transition. |

## Package status and authority boundary

This file belongs to the **Candidate-Neutral Building-Block Authority v3.3.2**.

The package is documentation-complete for the current development architecture, but it is not protocol-frozen and not canonically ratified. Technical results generated under it remain development evidence until the control suite, enumeration test, and hostile review pass.

The controlling package authorities are:

- `EVIDENCE_DISCHARGE_REGISTRY_V3_3_2.md`;
- `QUANTITATIVE_STOPPING_AND_EXHAUSTION_RULE_V3_3_2.md`;
- `MANDATORY_CONTROL_SUITE_V3_3_2.md`;
- `MIGRATION_AND_SUPERSESSION_RECORD_V3_3.md`.

A block is standalone for its owned object: it includes its complete definitions, interfaces, certificates, falsifiers, and owned evidence criteria. The full cross-block registry is intentionally stored once rather than repeated verbatim in every block.

### Shared status grammar