Purpose and claim boundary

This dossier reconstructs, at quark-sector resolution, the chain that the current GUT.md uses to move from the frozen Shape to the six quark masses, the CKM matrix, the CKM phase, and the Jarlskog invariant. The goal is not to replace the source manuscript. It is to make the quark mechanism reviewable as a single end-to-end object in the same spirit that Appendix D makes Standard-Model gauge recovery reviewable as one object.

The reconstruction is deliberately source-controlled. When GUT.md states a formula, value, hierarchy, hash, or status, this dossier preserves it. When the source contains an inconsistency, an omitted derivation, or a claim that relies on machine artifacts not present in the supplied file, the dossier does not silently repair it. Those items are elevated into an explicit technical-debt and falsification ledger.

The complete claimed forward map

The crucial methodological distinction is between routing and flavor. The Stage and Standard-Model backbone determine what a quark is allowed to be: color triplet, weak doublet/singlet structure, hypercharge, chirality, family multiplicity, and gauge consistency. They do not by themselves determine the observed mass hierarchy or CKM misalignment. The source explicitly introduces the finite, non-propagating chamber F+ to supply that missing flavor structure.

1.1 Active geometric support

The current branch uses the thirteen-dimensional propagating Stage built from ordinary spacetime and three compact carriers, with the finite flavor chamber classified separately as non-metric operator data. For the quark reconstruction the important point is not the headline dimension count by itself; it is that different physical obligations are routed to different factors.

1.2 Gauge algebra before masses

Appendix D treats this as the gauge-recovery certificate. The quark flavor dossier must inherit this output rather than re-assume it. The flavor chamber is therefore downstream of a previously typed quark field content: left-handed quark doublets and right-handed up/down singlets already know their gauge representation before any Yukawa operator is evaluated.

1.3 Quark representations and electric charge

This matters for flavor because the Yukawa map is not being applied to arbitrary three-component vectors. It acts on already identified up- and down-type quark sectors with fixed gauge quantum numbers. A reviewer should therefore separate “why there are up and down quark sectors with these charges” from “why their masses and mixing take these values.” The first is Standard-Model routing; the second is the F+ flavor problem.

2.1 Three families are a prerequisite, not a fit parameter

A 3x3 Yukawa construction only makes physical sense after the theory has supplied a three-dimensional family multiplicity space. GUT.md routes this through the K6/spin-C structure and records a three-family result upstream of the flavor chamber. The flavor chamber then instantiates

The conceptual discipline is important: the number 3 is not introduced because the observed CKM matrix is 3x3. The source intends the generation-space dimension to be inherited from the prior family result. F+ consumes that multiplicity; it does not create a new adjustable family count.

2.2 Sector projectors

For quarks, Pi_u and Pi_d create distinct operator domains inside the same generation space. This separation is load-bearing: an up-type hierarchy and a down-type hierarchy are allowed to be structurally different while still sharing the same family multiplicity. It also prevents an arbitrary single 3x3 matrix from silently serving every flavor sector.

2.3 What is and is not achieved at this point

This boundary is exactly why a separate quark dossier is useful. Standard-Model reconstruction gets the theory to the entrance of flavor. It does not cross the flavor gate.

3.1 The unsolved problem after gauge reconstruction

Once the gauge and family structure is fixed, the quark sector still contains two qualitatively different forms of structure: very strong hierarchies of singular values inside the up and down sectors, and a small but nontrivial misalignment between their left-handed eigenbases. CP violation adds a phase invariant that cannot be obtained from a purely real aligned construction.

GUT.md explicitly says the pre-flavor backbone cannot close this problem without additional structure. That statement is significant because it prevents the later chamber from being advertised as though every quark observable had already followed from the bare product manifold.

3.2 Minimal jobs assigned to F+

1. supply a finite three-generation operator space rather than another propagating metric factor;
2. separate up and down projected sectors;
3. supply target-blind discrete action ladders that generate repeated hierarchy ratios;
4. supply a phase rule tied to the order-three fixed point;
5. allow only sector-level normalizations, forbidding one normalization per family;
6. supply a deterministic map from chamber operators to Yukawa matrices;
7. supply one continuous frame-misalignment parameter theta_F, explicitly counted as calibrated by |V_us|.

4.1 F+ is not an extra metric dimension

The full-precision source classifies F+ as finite/algebraic/spectral/operator data. It carries a modulus and a derived Cartan-torus radius as chamber data, but no independent KK tower and no addition to the propagating dimension count. The active branch therefore remains 13-dimensional at the metric level.

4.2 Exact chamber tuple

5.1 Order-three fixed point and the common hierarchy scalar

Independent evaluation of the printed expression gives kappa = 0.004333420509983. The full-precision A1.13 table agrees with this value. Some lower-precision narrative passages print 4.3286e-3; the high-precision authority is the value above.

5.2 Why a single scalar can generate two hierarchies

The source does not assign three unrelated Yukawa eigenvalues to each sector. It assigns one common scalar kappa and a sector-specific vector of exact rational exponents. This converts the hierarchy problem into a ladder-selection problem.

That is the core parameter-collapse mechanism in the quark sector. A generic diagonal up/down pair has six independent positive eigenvalues before normalization. The chamber replaces their relative structure by one common scalar plus two discrete exponent triples.

6.1 Up-type ladder

The source describes this ladder as lexicographically minimal on its declared rational A2 ladder family. The target-blindness of that selection is a provenance claim; the numerical consequences of the ladder are independently checkable immediately.

6.2 Exact hierarchy ratios

These two masses are therefore not independent knobs once the top scale is fixed. This is one of the strongest self-contained pieces of the quark reconstruction because the calculation can be reproduced from the printed equations alone.

6.3 Up-sector normalization

The source counts y_t(M_Z)=0.9665 as a declared anchor and uses it to pin the heavy up-sector scale. In the R1.8 convention this corresponds to m_t(M_Z)=168.26 GeV. The distinction matters: m_t is not an additional independent prediction if y_t is the anchor expressed as a mass.

7.1 Down-type ladder

The source describes this ladder as selected on affine A2 Dynkin nodes. Conditional on the heavy down-sector scale, the strange and down masses are fixed by the exact same hierarchy scalar used in the up sector.

Again the relative hierarchy is independently reproducible. The nontrivial issue is the provenance of the heavy down-sector scale itself, treated in the next chapter.

8.1 The source gives two incompatible provenance stories for N_d

This is the single most important audit finding in the dedicated quark reconstruction. In the main fixing narrative, N_d=0.024 is said to arrive “from the geometry, not from a third measurement,” via the finite determinant eta_BK, the K_tb correction and RG running. But the binding full-precision A1.13 table says N_d is “defined to set m_b to its target value at M_Z.” Appendix J.6 even labels the exact bottom-mass hit as an “N_d normalization anchor.” These statements cannot all be true in the same parameter-counting sense.

8.2 What can be independently checked today

Using the full-precision value eta_BK=0.009721281516312024 gives 1/eta_BK = 102.867096104771, agreeing with the printed raw determinant ~102.87. Likewise K_tb^crit=exp(-pi sqrt(3)/16) evaluates to 0.711708130424.

What is not present as a self-contained printed derivation is the complete map from the raw determinant 102.87 through the K_tb/R_tb running to the claimed M_Z ratio 57.50, and then from that ratio to N_d=0.024 under a convention consistent with J.6. The manuscript points to machine artifacts/reproduce_all.py, but the supplied GUT.md alone is not enough to re-run that chain.

8.3 Required repair for full rigor

1. Write the complete symbolic relation y_t/y_b(raw) -> K_tb/R_tb -> y_t/y_b(M_Z) with every factor and convention explicit.
2. Derive N_d from that relation without loading m_b or y_b as a target.
3. Run the derivation blind to the bottom mass and publish the input manifest/hash before comparison.
4. Delete or correct the A1.13 language saying N_d is defined to hit m_b if the blind derivation succeeds.
5. If the blind derivation does not succeed, count N_d/m_b as an additional quark anchor and downgrade the compression claim accordingly.

9.1 Deterministic Yukawa map

This rule is the central anti-smuggling constraint. The source forbids independent family normalizations N_{s,a}. Therefore a 3x3 Yukawa matrix is not allowed to acquire nine arbitrary complex entries. It must be generated from the chamber operator evaluated in the frozen generation basis, with one scalar normalization per sector.

9.2 Canonical chamber-basis matrices

The full-precision A1.13 source actually folds N_s into the printed O_s matrix, while Appendix J writes the operator shape first and then multiplies by N_s. This is mostly a notation/ownership distinction as long as N_s is counted consistently. For auditability, the dedicated dossier keeps “shape eigenvalues” and “sector normalization” conceptually separate.

9.3 Parameter count at this stage

10.1 Singular-value diagonalization

The mathematical point is standard but crucial for the claim: masses are not read from arbitrary matrix entries. They are basis-invariant singular values. If a chamber-frame rotation changes matrix entries without changing singular values, it changes mixing information but not the mass spectrum.

10.2 Up alignment

At tau=omega the source chooses the up-sector chamber frame to coincide with the mass eigenbasis. This makes the relative mixing entirely a down-sector effect in the adopted convention.

10.3 Down frame

GUT.md states this structure but does not print the complete numerical generator J_DFT or the final matrix entries in the main text; it points to certificates/operators_Fplus.json. Therefore the form of the one-angle rule is source-supported, while a fully independent matrix-level replay requires the referenced certificate artifact.

11.1 CKM as relative rotation

The second declared quark anchor is |V_us|=0.22436. The source uses it to solve for the single real chamber angle theta_F. After that fixing, the remaining CKM magnitudes are treated as outputs of the same down-sector unitary.

11.2 Numerical CKM magnitude table from Appendix J

11.3 Magnitude-only unitarity sanity check

A unitary matrix must have row and column norm one. Magnitudes alone do not test orthogonality phases, but they do provide a basic consistency check. Squaring the printed magnitudes gives:

The deviations are at the few-parts-in-a-million level, consistent with rounding of a unitary matrix. This does not independently prove the DFT-Z3 construction, but it shows that the printed magnitude table is internally compatible with unitarity at its displayed precision.

12.1 Holonomy phase

The source then compares a Wolfenstein-aligned convention of +60 degrees to the PDG phase convention. The raw holonomy and the comparison convention must be kept distinct; the manuscript itself contains a countersign history correcting an earlier -60 degree arithmetic display.

12.2 Jarlskog invariant

Appendix J reports J_CKM=(2.92 +/- 0.40)e-5 against the comparison value (3.00 +/- 0.13)e-5. Because the full complex CKM entries are not printed in GUT.md, this number cannot be independently regenerated from the magnitude table and phase statement alone without the exact convention/matrix artifact. It is therefore source-certified but not independently replayed in this dossier.

12.3 What would falsify the phase story

• If the order-three holonomy does not force the stated phase under a clean convention map, the CP claim loses its geometric basis.
• If theta_F or another hidden phase is adjusted after the CP comparison, the anti-fitting firewall is violated.
• If a rephasing-consistent reconstruction of the referenced operator file produces a materially different Jarlskog invariant, Appendix J must downgrade.

13.1 Comparison scale

The source declares two-loop Standard-Model MSbar transport to the Z mass as a frozen rule. This prevents a common flavor-model failure mode: shifting the comparison scale after seeing which scale makes a mass look better.

13.2 What this dossier can and cannot replay

The algebraic hierarchy ratios can be replayed directly. The two-loop RG transport itself is not printed as an executable beta-function implementation in GUT.md, and the referenced reproduce_all.py / certificate files are not embedded in the single source file. Therefore this dossier records the RG interface as a frozen dependency rather than pretending to have independently rerun it.

14.1 Appendix-J numerical ledger

The following table is transcribed from the current Appendix J authority, with one additional “audit note” column distinguishing the source’s claimed output status from the provenance issue identified in this dossier.

14.2 Authority conflict on the up-quark pull

Section 7/8 narrative still calls m_u a ~4.4 sigma weakest link, whereas the controlling J.6 table reports a pull of 1.26 under the current theory band. Under GUT.md’s own authority hierarchy, Appendix J controls the numerical certificate. The dedicated dossier therefore uses 1.26 and labels the 4.4-sigma sentence stale narrative debt.

14.3 Interpretation of agreement

The theory bands are much broader than current experimental uncertainties for several light-quark observables. Agreement inside those bands therefore establishes only compatibility at the declared structural precision. It is not precision flavor prediction at the PDG uncertainty scale. A rigorous public claim should state the theory uncertainty next to every comparison, exactly as J.6 does.

15.1 The advertised compression

GUT.md counts y_t and |V_us| as the two quark anchors and excludes m_t as merely the y_t anchor expressed as a mass. The claimed 13 outputs then include the remaining mass information, the between-sector ratio, independent CKM information, the CP phase and Jarlskog invariant.

15.2 Why family-level normalization is forbidden

If the model allowed N_{u,1},N_{u,2},N_{u,3} and analogous down-sector constants, then the observed hierarchy could be reproduced trivially. The source therefore makes family-level normalizations inadmissible. This is a genuine and useful firewall.

15.3 But a sector normalization can still be an input

The fact that N_d is one scalar rather than three does not automatically make it geometric. If N_d was chosen to hit m_b, it is still calibration information. The correct compression count would then increase by one quark input. This is why the A1.13 provenance conflict is not cosmetic: it changes the interpretation of the “two in, thirteen out” headline.

15.4 Conservative parameter-count ledger

16.1 Freeze-before-compare is the correct control

The manuscript’s strongest methodological idea is that chamber objects should be hashed/frozen before comparison outputs are loaded. If the exact object descriptions and machine artifacts genuinely predate the comparisons, then post-hoc movement is mechanically constrained rather than merely denied.

16.2 What the hash does and does not prove

A content hash proves object identity once the object is published. It does not by itself prove that the object was selected without target information. That second claim requires chronology/provenance: the selection inputs and candidate-elimination record must also be frozen or independently reconstructible.

16.3 Target leakage tests for quark reconstruction

1. Verify that a_u and a_d selection code never reads quark-mass targets.
2. Verify that eta_BK and K_tb definitions do not import y_b or m_b.
3. Verify that theta_F reads only |V_us| and no other CKM entry.
4. Verify that the phase rule is fixed by holonomy and not by delta_CKM.
5. Verify that the RG scale/scheme is frozen before all mass comparisons.
6. Re-run on blinded comparison targets and compare hashes.

17.1 Component ledger

17.2 What “load-bearing” should mean here

For quark reconstruction, a component is load-bearing if removing it while holding the remaining source rules fixed makes at least one previously generated invariant undefined or forces the introduction of a new independent datum. This is weaker than proving uniqueness but stronger than saying the component appears in the notation.

17.3 Strongest current load-bearing links

• a_u and kappa are strongly load-bearing for the up hierarchy because the printed equations directly fix two independent mass ratios.
• a_d and kappa are strongly load-bearing for the down hierarchy conditional on the heavy down scale.
• theta_F is load-bearing for the one-angle CKM construction by definition of the source pipeline, though exact matrix-level replay requires the referenced operator artifact.
• the holonomy is load-bearing for the source’s CP-origin claim; without it the phase would need a new source.
• the anti-fitting rule is epistemically load-bearing: without it the same numerical table could be generated by per-family tuning.

18.1 Ablation tests that would convince a hostile reviewer

18.2 Restoration control

The restoration leg is essential. If returning the original frozen object does not restore the original outputs, the apparent ablation effect is likely implementation drift rather than a causal property of the Shape.

19.1 Internal contradictions and missing bridges

19.2 Projector-domain issue deserves special attention

The full-precision table states that G_gen is three-dimensional and also describes Pi_u, Pi_d, Pi_e, Pi_nu as orthogonal rank-3 maps on G_gen satisfying Pi_i Pi_j=delta_ij Pi_i. Four nonzero mutually orthogonal rank-3 projectors cannot coexist on a single three-dimensional vector space. The likely intended object is a direct sum of four sector copies of the generation space, but that enlarged domain must be written explicitly. This is a mathematical typing issue, not a numerical quibble.

The equation above is a proposed clarification, not something this dossier attributes to GUT.md. It is included to show the minimal mathematical structure that would make the advertised projector algebra coherent. The final authority should either adopt an equivalent domain or state the actual one.

20.1 What is already unusually strong

• The up hierarchy is a compact and directly replayable consequence of one exact ladder and one fixed-point exponential.
• The down hierarchy uses the same scalar with a different exact rational ladder, producing the printed m_s and m_d conditional on the bottom scale.
• The CKM magnitudes form an internally unitary-looking matrix at displayed precision and are generated under a one-angle narrative rather than nine independently tuned magnitudes.
• The CP phase is tied to a discrete order-three holonomy rather than treated as an arbitrary continuous phase.
• The source explicitly forbids family-level normalization and post-comparison reopening.

20.2 What must be fixed before claiming full-rigor reconstruction

1. Resolve N_d provenance and recompute it blind.
2. Publish the exact DFT-Z3 generator, theta_F solution and complete complex CKM matrix calculation.
3. Clarify the projector domains/ranks.
4. Package the two-loop RG reproducer and the exact input manifest with deterministic environment.
5. Reconcile stale numerical narratives against the controlling Appendix J table.
6. Run a blinded independent reproduction by an agent that sees the frozen Shape and code but not the quark comparison targets.

21.1 Minimum reproduction package

21.2 Blind run order

1. Load Shape and F+ objects without comparison targets.
2. Derive kappa and both action-ladder operators.
3. Apply only the declared calibration input(s).
4. Generate Y_u,Y_d and solve theta_F from |V_us| if that anchor remains in scope.
5. Run RG transport to M_Z.
6. Commit output hash.
7. Only then open comparison_targets.json.
8. Compute residuals and publish every row, including failures.

21.3 Decisive N_d fork

22.1 Independent arithmetic certificate included in this dossier

These checks are generated directly by this document builder from the printed formulas. They are not copied from the J.6 table. Their agreement with the source is therefore a small but genuine independent replay of the algebraic core.

22.2 What is deliberately not certified by this arithmetic replay

• the origin/selection proof for a_u or a_d;
• the bottom-scale N_d derivation;
• the exact complex CKM matrix;
• the Jarlskog phase convention;
• the two-loop RG evolution;
• the source chronology that establishes target-blind chamber selection.

23.1 Up-hierarchy lemma (conditional on source primitives)

23.2 Down-hierarchy lemma

23.3 Mixing proposition

23.4 CP proposition

23.5 Compression theorem claim versus established arithmetic

24.1 Gate-style closure ledger

24.2 Why this is a stronger dossier than a simple success table

The quark construction is most persuasive when its algebraic successes and unresolved provenance are shown on the same page. A theoretical reviewer can then attack the actual load-bearing links rather than arguing about rhetoric. If QK-05 closes target-blind and the matrix/RG artifacts reproduce independently, the dossier can be upgraded without changing its architecture; if they fail, the exact downgrade is already specified.

25.1 Observable-by-observable dependency graph

A reconstruction is only as rigorous as its dependency bookkeeping. The table below treats every quark observable as the terminus of a directed path. It deliberately distinguishes an anchor from a generated ratio, and it distinguishes a source-carried statement from a calculation that can be independently replayed from the equations printed in GUT.md.

25.2 Algebraic dependency graph

This compact arrow is not intended to hide the two calibrations or the disputed down normalization. A more honest factorization is

The question mark on N_d is the central provenance question. If a blind determinant/RG calculation supplies N_d, it moves to the first geometric block. If m_b or y_b must be read to choose it, it belongs with the calibration inputs. No other interpretation should be permitted in the final ledger.

25.3 Independence classes

The source naturally divides the quark claims into four independence classes. Class A contains algebraic consequences that can be recomputed from a few printed constants. Class B contains calculations whose formulas are stated but whose exact numerical operator artifact is external to this standalone file. Class C contains claims that depend on a transport or determinant chain not printed end-to-end. Class D contains measurement anchors. Mixing these classes in one undifferentiated prediction count would overstate the evidence.

25.4 Why this graph matters

If an outside reviewer breaks a Class-A link, the basic hierarchy mechanism fails. If Class A survives but the exact matrix artifact fails, the hierarchy result remains while the CKM certificate downgrades. If the N_d bridge fails, the down-sector ratios still survive but the absolute down-sector scale becomes calibrated rather than generated. This modular downgrade behavior is a strength: it prevents one unresolved link from either being hidden or unnecessarily destroying results that do not depend on it.

26.1 The precise question

The decisive unresolved quark question is not whether N_d=0.024 reproduces m_b. It plainly does in the source table. The question is whether the value can be obtained without loading m_b, y_b, or a quantity already calibrated to them. The blind experiment therefore treats the bottom measurement as cryptographically unavailable until after the predicted N_d has been committed.

26.2 Inputs allowed before the blind seal opens

26.3 Inputs forbidden before commitment

• m_b(M_Z) or any equivalent bottom-mass target;
• y_b(M_Z) or a table from which it is trivially reconstructed;
• the target ratio |y_t/y_b|(M_Z);
• N_d=0.024 itself, unless it is being checked as the claimed output rather than loaded as a primitive;
• a fitted R_tb or threshold coefficient whose provenance used the bottom target.

26.4 Required derivation chain

Every arrow must be an explicit function with a frozen provenance record. A statement such as running brings 102.87 to 57.50 is not enough for a certificate. The executable must show the exact transformation, the scale at which each factor is defined, and which variables were optimized, if any.

26.5 Commitment protocol

1. Prepare a target file containing m_b, y_b and the comparison ratio; hash and withhold it from the reproducing agent.
2. Run the determinant and RG chain using only the allowed manifest.
3. Write predicted N_d, y_b and m_b to an output artifact and commit its SHA-256.
4. Open the target file only after the output hash exists.
5. Compute residuals without changing any upstream value.
6. Repeat under small numerical-tolerance perturbations to distinguish a stable result from accidental solver tuning.

26.6 Pass, partial pass, and fail states

26.7 Why a failure would still leave useful physics

Failure of the blind N_d test would not erase the common hierarchy scalar or the rational down ladder. The conditional equations m_s/m_b=kappa^(2/3) and m_d/m_b=kappa^(4/3) remain independent algebraic statements. What changes is the input count and the interpretation of the heavy down scale. This is exactly why the dossier separates absolute scales from within-sector shapes.

27.1 What is source-derived and what is standard mathematical scaffolding

GUT.md states that the down diagonalizer belongs to a DFT-on-Z3 family and is rotated by one angle theta_F. It does not, in the standalone source used for this dossier, print the full numerical generator used by the machine certificate. The equations below therefore provide standard Z3 Fourier mathematics as a reproduction scaffold; they are not asserted to be byte-identical to the unpublished operator artifact.

27.2 Canonical Z3 Fourier transform

Any source claim described as DFT-on-Z3 should state whether its W_DFT is F_3 itself, a column/row permutation, a rephased equivalent, or a different representation. Those choices can leave some magnitudes invariant while changing phase conventions, so they cannot be left implicit when the Jarlskog invariant is part of the certificate.

27.3 One-parameter unitary family

To make the one-angle claim independently executable, the final certificate needs the Hermitian generator J (or an algebraically equivalent explicit R(theta)), the exact W_DFT convention, and the phase/rephasing convention used before comparing delta_CKM. Without those data, the statement is a well-defined architecture but not a self-contained numerical reproducer.

27.4 Overconstraint test for one-angle mixing

The scientific value of the one-angle architecture is not that one angle can hit |V_us|; by construction it can. The value is that the same angle must then land the remaining CKM magnitudes and phase-related invariants without further continuous adjustments. Let f_ij(theta) denote the magnitude produced by the frozen family. Once theta is solved from f_us(theta)=0.22436, every other f_ij is a prediction of that family.

A rigorous certificate should therefore publish the scalar root-finding residual for the anchor, all eight held-out magnitude residuals, the complex-unitarity residual ||V^dagger V-I||, and J_CKM computed from the unrephased complex matrix. This turns one angle from a narrative compression claim into an overdetermined numerical test.

27.5 Rephasing and CP

Quark-field rephasings can change the displayed phases of individual CKM entries without changing physical invariants. A robust certificate should therefore compare rephasing-invariant quantities such as |V_ij| and J_CKM, and should state exactly how the raw -2pi/3 holonomy is mapped into the convention in which the source quotes a +60 degree comparison phase. The arithmetic identity -2pi/3=-120 degrees must never again be conflated with -60 degrees; the GUT archive itself records that earlier presentation error.

27.6 Minimum exact artifact

{
  "omega": "exact algebraic or high-precision complex value",
  "W_DFT": [["complex", "..."], ["..."], ["..."]],
  "J_DFT_Z3": [["complex", "..."], ["..."], ["..."]],
  "theta_F": "high precision",
  "U_u": [["complex", "..."]],
  "U_d": [["complex", "..."]],
  "V_CKM": [["complex", "..."]],
  "unitarity_residual": "...",
  "J_CKM": "...",
  "phase_convention": "explicit"
}

28.1 Logarithmic sensitivity of the hierarchy

Because the mass hierarchy is exponential, the cleanest sensitivity variables are logarithms. For a chamber eigenvalue y_a=N kappa^a, the exact differential is

Thus the exponent itself is the logarithmic sensitivity to kappa. This gives a transparent way to propagate uncertainty in the geometric hierarchy scalar without Monte Carlo machinery.

28.2 Sensitivity to the exponential action

A perturbation delta-lambda therefore induces delta-y/y approximately -a delta-lambda. The rigid rational exponents make a specific correlated-error pattern: an error in the common geometric action moves charm and up by factors 1 and 2 in log space, while strange and down move by 2/3 and 4/3. This correlation is itself a falsifiable signature of the shared-kappa hypothesis.

28.3 Ratio invariants eliminate sector normalizations

These four quantities are particularly valuable because N_u and N_d cancel. Even if the down absolute-scale provenance remains unresolved, the two down ratios can be tested without deciding whether N_d is geometric or calibrated. They should be the first quantities used in an independent blind hierarchy test.

28.4 Cross-sector invariant implied by the shared scalar

This equality is a compact cross-sector diagnostic of the rigid ladder. It follows from the printed exponents alone. It does not depend on N_u or N_d, so it is immune to the bottom-scale provenance dispute. In a future target-blind run the four independently reconstructed ratios can be transformed back into four estimates of kappa; agreement is a sharper test than quoting each mass separately.

28.5 Uncertainty propagation

For small independent uncertainties in N and kappa, first-order propagation gives

The covariance term should not be set to zero automatically if N or the RG factors are generated from the same chamber data. A rigorous uncertainty budget therefore needs provenance-aware covariance, not independent ad hoc theory bands attached to each observable after the fact.

28.6 Sensitivity matrix as a reviewer artifact

The final machine certificate should export a Jacobian whose rows are quark observables and whose columns are every admitted primitive/calibration. Singular-value analysis of that Jacobian would show which claimed outputs are genuinely independent and which are nearly the same piece of information repeated in different units.

29.1 Why parameter counting must be done carefully

The source compression claim is meaningful only if every effective degree of freedom is counted once. Counting two declared measurements while silently treating N_d, an unspecified DFT generator, or tunable RG factors as fixed geometry would undercount the model. Conversely, counting algebraically fixed matrix entries as independent parameters would unfairly penalize the construction.

29.2 Standard quark-sector reference count

As standard field-theory bookkeeping, two unconstrained complex 3x3 Yukawa matrices contain 36 real numbers before flavor-basis redundancies are removed. After the allowed quark-field basis transformations, the physical quark sector is summarized by ten observables: six masses, three mixing angles, and one CP-violating phase. This standard count is used here only as a reference for compression; it is not a statement found in GUT.md.

29.3 Shape construction count

29.4 Compression score with the N_d fork

If the source strongest provenance story survives, the continuously calibrated quark coordinates are y_t and |V_us|, with the remaining structure frozen upstream. If N_d is target-set, the quark calibration count is at least three. The difference matters, but either outcome is still a substantial reduction relative to freely specifying the physical ten-observable quark sector. The correct scientific claim should therefore report both the raw parameter count and the provenance-qualified count.

29.5 Information leakage audit

A discrete ladder selected after seeing the six quark masses can encode target information even if it contains no continuous parameter. Parameter counting alone cannot detect this. The freeze chronology must therefore be audited: when were a_u and a_d selected, what candidate family was searched, what objective was visible, and were quark targets hidden? A low-dimensional formula chosen after looking at the answer is compression, but not prediction.

29.6 Minimum description length perspective

A useful supplementary statistic is description length: how many bits are required to specify the admitted quark mechanism, including discrete model choices, versus an unconstrained table at the same numerical precision? This does not prove physical truth, but it makes hidden complexity visible. The description must include the ladder-selection rule, projector domains, DFT generator, phase convention, RG code version and any threshold choices - not only the two headline numerical anchors.

30.1 Hostile-review sequence

A reviewer should not begin by debating whether the whole geometry is plausible. The efficient attack is to test the smallest load-bearing facts in an order that maximizes information gain. The following sequence is designed so an early failure produces a precise downgrade rather than an argument about the whole program.

30.2 No single number is enough

The quark mechanism is compelling only as a pattern: one exact exponential controls four ratios; two rational ladders distinguish up and down sectors; one frame angle controls multiple mixing magnitudes; one discrete phase controls CP; and the same machinery obeys an anti-fitting rule. Agreement of only one or two outputs would be easy to obtain accidentally. The dossier therefore treats the joint dependency pattern as the evidentiary object.

30.3 Strong falsifiers

• A blinded recomputation of the ladder-selection rule chooses different exponents once quark targets are hidden.
• The four ratio-derived estimates of kappa disagree beyond the preregistered uncertainty model.
• N_d cannot be obtained without bottom data despite being called geometric.
• The explicit one-angle DFT family cannot reproduce the held-out CKM magnitudes in the controlling certificate.
• The raw holonomy phase cannot reproduce J_CKM under a consistent rephasing convention.
• The advertised projector algebra has no coherent domain compatible with all stated ranks/orthogonality identities.

30.4 Strong positive outcome

The strongest credible outcome is not quarks prove the geometry. It is a target-blind, independently replayed certificate in which a small frozen geometric/operator package generates a much larger set of quark invariants, every hidden degree of freedom is charged, ablations have specific reversible effects, and the weakest numerical row is retained rather than tuned away. That would be strong cross-layer evidence that the Shape is genuinely carrying information.

30.5 Reviewer sign-off block

Independent reviewer: ____________________________
Implementation/environment hash: ____________________
Targets hidden until output commit?  YES / NO
N_d blind derivation: PASS / PARTIAL / FAIL
Projector typing: PASS / FAIL
Exact CKM replay: PASS / FAIL
CP invariant replay: PASS / FAIL
RG replay: PASS / FAIL
Ablation/restoration: PASS / FAIL
Overall quark certificate: ACCEPT / CONDITIONAL / REJECT
Notes / first broken dependency: ______________________