UQF-14 — Unitarity / causality / locality: the gate anchor ledger

The honest one-line: UQF-14 is an audit/routing node with no internal target to derive and no internal axiom to close — it banks three real, in-scope perturbative + finite-Kaluza–Klein certificates (cluster decomposition, ghost decoupling, all-orders microcausality) plus one measured graviton-speed anchor ($10^{-15}$-level, GW170817/GRB170817A), and on the live board the gate stands RESOLVED +0 (CERTIFIED-IRREDUCIBLE, ratified 2026-07-08); in the frozen mid-audit record the roll-up was carried OPEN, set by the weakest of four inherited-open legs that are exported to the upstream gates that own them — those legs remain shown unchanged.

This page is the gate-specific instantiation of the anchoring method: it takes the master anchor and the four bridges and applies them, object by object, to one gate. Every exact thing UQF-14 touches gets its own row — its status, what it is allowed to claim, and what it is forbidden to claim. It follows the same eleven-part shape and the same universal table as the canonical SG-4 ledger.

selection ≠ derivation · given-E ≠ derivation-of-E · frozen/reproducible ≠ proven-unique.

1. Gate status header

• Gate-level UQF-14 roll-up: CERTIFIED-IRREDUCIBLE — RESOLVED +0 on the live board (ratified 2026-07-08). Frozen mid-audit reading: AUDIT (OPEN) (status = least-closed residual under the superseded rule, set by the weakest inherited link).
• Taxonomy reconciliation (2026-07-05): under the ratified closure taxonomy (board 2026-07-08) the gate-level grading is CERTIFIED-IRREDUCIBLE — RESOLVED +0, read as TERMINAL + RESIDUALS-SHOWN — the terminal is reached on the inherited Clay-class UV wall (the R1/R2 legs) while the residual family in this ledger (R1, R2, R3, R4, H5, H6) remains listed and carried unchanged. The facts are unchanged: the earlier AUDIT (OPEN) roll-up above reflects the superseded least-closed-residual rule, not a different set of facts. No individual residual is deleted, closed, or re-graded.
• The structural fact first: UQF-14 is not a single-number gate. It has no internal target to derive and no internal axiom to close — it is an audit/routing node whose verdict is the weakest of its inherited dependencies. The honest, non-promoting win it delivers is precision about which sub-claim is banked and which is inherited-open.
• The decisive collapse (the gate's local construction). Unitarity, causality, and locality are not three independent proof obligations; they are three faces of a single causal-net class-membership statement — that the descended 4D theory is a member of the standard axiomatic-QFT class (a Poincaré-covariant net of observable algebras with a positive-definite physical state space, spacelike-commuting observables, and an energy-positivity / spectrum condition). That class-membership statement, given the observed Standard-Model content $E$, is established below the cutoff at finite Kaluza–Klein truncation from 13D locality: $$ \big[\,\text{unitarity}\ \wedge\ \text{causality}\ \wedge\ \text{locality}\,\big]\ \Longleftarrow\ \mathcal{C}\!\text{-net membership}(E_{\rm frozen})\ \ \text{below cutoff, finite KK}, $$ which is recorded publicly as a DERIVED-GIVEN-E conjecture / theorem-debt, never as a finished theorem.
• Status, split so it cannot be misread:
  • Banked legs R5, R6, R7 (cluster decomposition; ghost decoupling; all-orders microcausality + the measured graviton-speed anchor): VERIFIED (banked) — standard QFT applied strictly inside its accepted scope (perturbative / finite-tower / below-cutoff), given $E$.
  • Inherited-open legs R1, R2, R3, R4 (above-cutoff graviton unitarity; nonperturbative strong-sector unitarity; full-tower cluster decomposition; nonperturbative electroweak): OPEN / EXPORTED to UQF-9, UQF-11/Gap-02, UQF-10, BG-10 — each of which carried AUDIT/OPEN in the same frozen mid-audit record (on the ratified board each stands RESOLVED +0, with these exported objects shown as its residuals).
  • Gate-level UQF-14: RESOLVED +0 (CERTIFIED-IRREDUCIBLE) on the ratified board; frozen mid-audit roll-up: AUDIT (OPEN). The badge is permanently EXPORTED to UQF-9 (R1 carries it). Direction: held. No individual leg status is upgraded.

Three banked legs are genuine in-scope verifications; under the superseded weakest-link min-rule they did not lift the mid-audit roll-up, which four inherited-open legs held at AUDIT (OPEN). On the ratified board the gate stands RESOLVED +0 (CERTIFIED-IRREDUCIBLE), with those legs shown as exported residuals.

selection ≠ derivation · given-E ≠ derivation-of-E · frozen/reproducible ≠ proven-unique.

2. Frozen inputs (what UQF-14 stands on, not what it produces)

• Frozen branch hashes dcc66f1b2685 (branch) / a5b1e6f9d951 (manifest meta). The branch is read-only and unmodified. These hashes are audit anchors — they certify which object was tested and that it cannot be quietly retuned. They do not validate the physics. A silent frozen-branch change is itself a falsification test trigger (→ refuted / restart).
• 13D locality is given. The 13D action is local in 13D — a property of the frozen construction, not a derived result. It enters UQF-14 as input. Locality in 13D plus finite-truncation locality in 4D does not establish locality with the full infinite KK tower.
• Upstream spectrum / content $E_{\rm frozen}$ is given / charged / inherited — the observed Standard-Model carrier content (graviton zero-mode, gluons, $W/Z$, photon, Higgs, chiral fermions, and their KK partners) enters as input. UQF-14 does not derive $E$. Every banked leg below is a statement about this $E$, not a derivation of it.
• BRST nilpotency $Q^2_{\rm BRST}=0$ of the descended 4D theory is inherited from UQF-4 (OPEN, no-known-route) — not a UQF-14 anchor. The ghost-decoupling bookkeeping presupposes it as a falsifier condition.

3. Object anchors (given-E / upstream)

The carrier coverage checklist the gate audits, all GIVEN-E / upstream-inherited (not UQF-14-derived):

$$ \underbrace{g_{\mu\nu}^{(0)}}_{\text{graviton zero-mode}},\ \ \{g_{\mu\nu}^{(n)}\}_{n\ge1}\ (\text{KK tower}),\ \ A_\mu^a\ (\text{gluons}),\ \ W^\pm_\mu,\ Z_\mu,\ \ A_\mu\ (\text{photon}),\ \ H,\ \ \{\psi_i\}\ (\text{chiral fermions} + \text{KK partners}). $$

Compactification supplying the descent: $K_6\times S^2\times S^1_Y/\mathbb{Z}_2$, integrated out per spacetime point. Status: GIVEN-E / upstream-inherited — not UQF-14-derived.

4. Root and master-anchor traceability

Deep roots that are load-bearing for UQF-14:

Master anchors in play: finite invariant ledgers (the per-sector ghost / commutator inventories) · no unpaid labels (every banked leg carries its explicit scope) · the frozen branch · given-$E$ · the declared structural posits (causal order, physical positivity, substrate) · the one measured invariant (the GW170817 / GRB170817A coincidence) · open-residual discipline (the weakest-link min-rule).

5. The UQF-14 anchor ledger (the universal table)

6. The construction — the collapse, the banked legs, the number hygiene

6.1 The decisive reduction (a collapse, not a stretch)

The most economical move is to drop the hidden "three independent guarantees" premise. Unitarity, causality, and locality are three observable consequences of one object — membership in the standard axiomatic-QFT class. The net reduction, recorded verbatim:

3 properties + 5 banked cancellation theorems → 1 class-membership statement, derived (given the observed Standard-Model content) by finite Kaluza–Klein truncation below the cutoff from 13-dimensional locality, resting on 2 named structural posits + 1 substrate posit + 1 measured anchor.

This is an economy of statement (a dissolution of false multiplicity), recorded as a DERIVED-GIVEN-E conjecture — dissolved ≠ solved.

6.2 The three banked legs, in scope

R5 — finite-truncation 4D EFT locality / cluster decomposition. A 13D-local action with the compact factors integrated out at finite KK truncation yields a 4D-local effective action obeying cluster decomposition, with only analytic $O(E^2/M_{\rm KK}^2)$ corrections — ordinary local higher-dimension operators, not genuine non-localities. With a local action, Lorentz covariance, and the spectral condition, cluster decomposition follows: correlation functions factorize at large spacelike separation. Scope: $E\ll M_{\rm KK}$. Modal status: DERIVED-GIVEN-E (perturbative / EFT).

R6 — per-sector perturbative ghost / unphysical-polarization decoupling on $\mathcal H_{\rm phys}=\ker Q_{\rm BRST}/\operatorname{im}Q_{\rm BRST}$, via the five banked cancellation theorems: Kugo–Ojima (gluons), Higgs mechanism + Equivalence Theorem ($W/Z$), Gupta–Bleuler / BRST (photon), spin-statistics with no surviving mirror fermions. Modal status: DERIVED-GIVEN-E and GIVEN AXIOM-PHYSICAL-POSITIVITY (perturbative kinematic positivity only). The load-bearing caveat: these theorems decouple the unphysical sector given a positive physical subspace; they do not establish that positivity. Nonperturbative 4D Yang–Mills positivity sits upstream of all five and is exported to R2.

R7 — perturbative all-orders microcausality + the measured graviton-speed anchor. (a) Each free-field carrier has a Pauli–Jordan / Proca / Klein–Gordon / Dirac commutator vanishing outside the lightcone, extended to all loop orders by Epstein–Glaser causal perturbation theory — kept perturbative (silent nonperturbatively / above-cutoff). (b) The measured graviton-speed anchor (see §6.3). Modal status: (a) DERIVED-GIVEN-E (perturbative); (b) measured-but-irreducible zero-mode anchor.

6.3 Number hygiene: the one measured invariant

The headline graviton-speed bound is $$ \frac{\lvert c_m - c\rvert}{c} < 10^{-15}, $$ from the near-simultaneous arrival of GW170817 and GRB170817A (two triggers $\sim1.7\,$s apart). This bound is not itself the measured atom. The bare measured invariant is narrower: two detector triggers $\sim1.7\,$s apart of laboratory clock time. Converting that coincidence into a fractional speed bound imports three named, non-irreducible co-premises that must travel with the number wherever it is shown:

1. a common-emission-time model (one source, bounded intrinsic emission-time offset);
2. the $\sim 40\,$Mpc baseline (a distance-ladder / redshift-inferred quantity);
3. shared causal order (needed even to call two propagation rates "equal").

The bare clock-coincidence is the measured atom; the speed bound is derived given those three co-premises. It is a single low-energy, single-baseline datum and cannot be promoted to cover the strongly-coupled, above-cutoff graviton sector (R1 / UQF-9).

6.4 The weakest-link split (the one honest table)

The badge is the weakest link. Three banked legs do not lift it; four inherited-open legs hold it at AUDIT (OPEN).

6.5 Diagnostic — the banking is specific, not a blanket pass

That the gate refuses to bank broadly is its specificity. The four falsification tests are each a forbidden cross: $$ \text{R5}\nRightarrow\text{R3},\qquad \text{R6}\nRightarrow\text{R2},\qquad \text{R7}\nRightarrow\text{R1},\qquad c_m\nRightarrow\text{full-QG causality}. $$ A blanket "unitary, causal, local" gate would have no such forbidden crosses. The presence of four sharp, named non-implications is what shows the banked set is scoped exactly to where standard QFT applies — not stretched across the cutoff. The dominant blind spot the discipline is built to catch is anchoring on the representation: treating the finite / perturbative / below-cutoff certificate as if it were the full / nonperturbative / above-cutoff physical theory.

7. Declared-structure splits (single phrases hiding multiple claims)

Two phrases carry more than one status and are split here:

1. "the theory is unitary, causal, and local." This hides (i) the banked below-cutoff / perturbative / finite-tower content (R5/R6/R7, DERIVED-GIVEN-E) and (ii) the open above-cutoff / nonperturbative / full-tower content (R1–R4, OPEN/EXPORTED). The honest reading is the §6.4 split, never the headline alone.
2. "cancellation on the physical Hilbert space" (R6). This hides (i) the decoupling of the unphysical sector (DERIVED-GIVEN-E, perturbative) and (ii) the positivity of that physical subspace (NOT established here; AXIOM-PHYSICAL-POSITIVITY, scoped to perturbative kinematics only, with nonperturbative positivity exported to R2). The decoupling is banked; the positivity is not.

A third phrase — "$\lvert c_m-c\rvert/c<10^{-15}$" — is split in §6.3 into the bare measured atom (irreducible) versus the three co-premises that make it a speed bound (not irreducible).

8. Open residuals — the inherited-open family and the two internal holes

Each residual is its own row; none is closed, and none is collapsed into a vague item.

Inherited-open family (sets the badge — each exported as a typed contract; all four upstream certificates currently MISSING):

• R1 — above-cutoff graviton-sector unitarity → UQF-9 (= B3, the universal UV wall). Owner standing AUDIT, certificate MISSING. This carries the badge. OPEN / EXPORTED. Flagged DO-NOT-CHASE: unicorn — above-cutoff unitarity cannot be settled until the UV completion is.
• R2 — nonperturbative strong-sector unitarity → UQF-11 / Gap-02 (Clay Yang–Mills mass gap). Owner standing Precisely-OPEN / AUDIT, certificate MISSING. OPEN / EXPORTED. Bounded target = the finite-resolution $z^\*<1$ gap (axiom-conditional on granularity P1); the continuum $a\to0$ uniform inequality is a retired continuum unicorn (REDUCED-TO-AXIOM, granularity) — do not target it as stated. Watch the hidden co-gate: 4D $SU(3)$ continuum-measure existence is a separate OPEN object.
• R3 — full infinite-KK-tower cluster decomposition → UQF-10 (downstream of UQF-9). Owner standing AUDIT, certificate MISSING. OPEN / EXPORTED. Falsifier = a tachyonic KK mode. The F1 shape-doublet saddle is LEANING REFUTED and must be reconciled first.
• R4 — nonperturbative electroweak (instantons / sphalerons) → BG-10. Owner standing 0-of-4 at certificate grade, certificate MISSING. OPEN / EXPORTED (scoped-out).

Internal / near-term holes (closeable without an upstream wall falling, or coupled to one):

• H5 — independent re-derivation of the U-AUDIT-B per-sector inventory. The negative-norm/ghost ledger, the commutator-vanishing ledger, and the per-sector audit-status matrix (cited to Q3 Appendix U) have not been independently re-derived for every carrier including all KK partners. OPEN. The one hole genuinely internal to UQF-14 — the cleanest near-term win; it corroborates (or refutes) R6/R7 directly and requires no upstream certificate.
• H6 — order-by-order BRST nilpotency of the descended 4D theory → UQF-4. $Q^2_{\rm BRST}=0$ at all loop orders is asserted as a falsifier condition but verified upstream only partially. OPEN. Routed to UQF-4 with a no-known-route caveat (the coset-twist / descended-anomaly construction has no short path today) — bounded, but not a near-term certainty.

9. Anti-claims (what this page refuses to say)

• UQF-14 does not derive $E$. The carrier content is the observed Standard-Model spectrum, given, not derived here.
• A banked perturbative leg is not a nonperturbative proof. Formally, the four forbidden crosses hold: $\text{R5}\nRightarrow\text{R3}$, $\text{R6}\nRightarrow\text{R2}$, $\text{R7}\nRightarrow\text{R1}$, $c_m\nRightarrow$ full-QG causality. Each is a RELABEL_FAIL if asserted.
• No above-cutoff unitarity proof. Above-cutoff graviton unitarity is conditional on UQF-9 and is not proven here — and is unprovable in principle for everyone, because it simply is the open UV-completion-of-gravity problem. Marking it a wall is the honesty, not a hedge.
• No nonperturbative strong-sector unitarity. Kugo–Ojima is perturbative and presupposes physical positivity; the nonperturbative certificate is the Clay mass gap.
• No full-tower cluster decomposition. Banked locality is the finite-truncation EFT statement; the infinite-tower claim is exported to UQF-10.
• No nonperturbative-EW disposition. Instantons/sphalerons are scoped out and exported to BG-10.
• The measured $c_m$ is a single low-energy, single-baseline zero-mode datum; it is not a quantum-gravity causality certificate, and it must never appear without its three co-premises.
• No $\Lambda$ / vacuum-energy / cosmological-constant cancellation — explicitly disclaimed; $\Lambda$ remains open (Weinberg-open).
• The frozen-branch hashes are audit anchors; they do not validate the physics.
• Audit-complete is not physically closed. The certificate wm1z47vzm (AUDIT_COMPLETE_OPEN) means the reduction reached its honest fixed point — bookkeeping stability, not closure. Convergence ≠ proof.

10. Specialist closure plan

There is no self-contained closure for UQF-14: the gate rises only as its upstream dependencies rise. The correct next move is the upstream bridge program, not re-attacking UQF-14. A refuting result is a valid close.

1. R1 / above-cutoff graviton unitarity (→ UQF-9 / B3). Build a UV-completion certificate — a truncation-independent non-Gaussian fixed point or a defensible non-continuum replacement — that validates above-cutoff graviton unitarity / Froissart-bound / Landau-pole control and passes the five-axiom mount test (MODAL STATUS must prove the above-cutoff class, not mere admissibility). Concretely-buildable sub-object on the frozen branch: the 6th heat-kernel coefficient $a_6$ (necessary-not-sufficient; currently AUDIT_UNVERIFIED — only the dimensionless ratio $124/315$ is clean; the order-6 mixed Neumann+Dirichlet boundary coefficient for $S^1_Y/\mathbb{Z}_2$ does not exist in the literature). Do not fabricate $a_6$ magnitudes or a positivity-functional pass. Highest-leverage node — R1 and R3 both bottom on B3. Refuting close: uncontrolled high-$E$ amplitudes, a negative-norm physical state above the cutoff, or a regulator-dependent conclusion.
2. R2 / nonperturbative strong-sector unitarity (→ UQF-11 / Gap-02). Deliver the bounded target — a finite-resolution ($z^\*<1$) spectral-gap result for $SU(3)$, axiom-conditional on granularity, with a negative control (the $\kappa^3/\pi$ lesson: do not let granularity make the result true-by-construction) — plus an explicit disposition of 4D $SU(3)$ measure-existence as its own object. Do not target the continuum $a\to0$ unicorn. The "uniform clustering ⇒ gap" implication is already rigorous; the open object is one marginal-coercivity inequality in the $d{=}4$ band. Refuting close: a negative-norm physical state survives confinement.
3. R3 / full-tower cluster decomposition (→ UQF-10). Build a compactification-stability certificate for the full KK tower — moduli mass-matrix positivity, no tachyonic/runaway modes, from a performed RG calculation — plus a proof that finite-truncation locality composes to the full tower. Reconcile the F1 shape-doublet saddle (LEANING REFUTED) first. Refuting close: a tachyonic KK mode.
4. R4 / nonperturbative electroweak (→ BG-10). Bring the nonperturbative EW sector in-scope and discharge the BG-10 sphaleron/instanton ledger at certificate grade (a finished, basis-invariant, anomaly-aware SMG-class treatment). Refuting close: a genuine nonperturbative-EW unitarity/causality violation.
5. H5 / U-AUDIT-B re-derivation (internal). Line-by-line audit reproducing the negative-norm/ghost and commutator-vanishing ledgers; confirm no carrier (especially KK partners) is missing and no entry is asserted without the explicit calculation. Refuting close: an asserted-but-false entry or a missing carrier → a real defect fed back to R6/R7.
6. H6 / BRST nilpotency (→ UQF-4, no-known-route caveat). Verify $Q^2_{\rm BRST}=0$ to the required loop order for the descended 4D theory. Refuting close: a nilpotency failure at some loop order → falsifies the unitarity sub-claim, propagated to UQF-4.

Closing the inherited legs upgrades UQF-14 only given $E$, and only as the upstream walls rise — no move inside UQF-14 lifts it.

11. Completion tests for this page

Tests passed (required presence, all met): gate roll-up RESOLVED +0 (frozen mid-audit reading: AUDIT (OPEN)) · the local construction as the $\mathcal{C}$-net class-membership statement, DERIVED-GIVEN-E (conjecture) · "$E$ not derived" · frozen hashes (AUDIT ONLY) · every exact object as its own row (R5; R6 + its five cancellation theorems; R7(a)+(b); R1–R4; U-AUDIT-B; BRST; certificate) · the measured graviton-speed anchor split into atom + three co-premises · the four-forbidden-cross specificity diagnostic · the weakest-link split table · every open residual (R1–R4, H5, H6) as its own row · the gate's anti-claims (banked-leg-not-nonperturbative, $c_m$-not-full-QG, audit-complete-not-closed).

Tests held (required absence, all held): no claim that UQF-14 is physics-closed · $E$ derived · a banked perturbative leg sold as a nonperturbative / above-cutoff proof · any forbidden cross ($\text{R5}\!\Rightarrow\!\text{R3}$, $\text{R6}\!\Rightarrow\!\text{R2}$, $\text{R7}\!\Rightarrow\!\text{R1}$, $c_m\!\Rightarrow$ full-QG) asserted · $c_m$ shown without its three co-premises · the continuum $a\to0$ inequality targeted as the R2 close-condition · audit-complete read as physically closed · convergence read as proof · hashes validate physics · a $\Lambda$ cancellation claim.

Open items: R1 (OPEN/EXPORTED → UQF-9, carries the badge) · R2 (OPEN/EXPORTED → Gap-02, bounded finite-resolution target) · R3 (OPEN/EXPORTED → UQF-10, tachyonic-KK falsifier) · R4 (OPEN/EXPORTED → BG-10, 0-of-4) · H5 (internal U-AUDIT-B re-derivation) · H6 (BRST nilpotency → UQF-4, no-known-route).

Assumptions made: none beyond the dossier — every status matches the dossier's frozen audit record (mid-audit roll-up AUDIT/OPEN under the superseded weakest-link min-rule — on the ratified board the gate stands RESOLVED +0, CERTIFIED-IRREDUCIBLE; R5/R6/R7 banked; R1–R4 exported-open; badge exported to UQF-9); every number ($10^{-15}$, $\sim1.7\,$s, $\sim40\,$Mpc, $124/315$) traces to the dossier or corpus; nothing fabricated; no status upgraded.

This gate anchor ledger follows the canonical eleven-part shape and universal table of the SG-4 ledger.

See also: the anchoring method · A0 — the master anchor · Layer 4 — carrier-forcing & the given-E wall (why the geometry is load-bearing but not certifying) · SG-4 — Hypercharge & anomaly (the canonical gate ledger) · UQF-3 — Reflection positivity / physical Hilbert space (the sibling positivity gate that R6 presupposes and R2 exports) · the full UQF-14 dossier.