A quantum field theory built on the frozen 13-dimensional geometry must respect the three pillars that make a quantum theory physically sane: unitarity (probabilities sum to one; no negative-norm states), causality (no influence outside the lightcone), and locality (a local action with cluster decomposition). This gate asks whether the descended four-dimensional theory inherits these properties not just at low energy, but all the way up — including above the perturbative cutoff where the graviton and the full Kaluza–Klein tower become strongly coupled.
The frozen geometry supplies the inputs to the audit, not its verdict. The 13D action is local in 13D; integrating out the compact factors (K₆ × S² × S¹) at each spacetime point yields a 4D effective action that is local at any finite KK truncation, with only analytic, EFT-suppressed (E²/M_KK²) corrections. Each descended carrier (graviton zero-mode, gluons, W/Z, photon, Higgs, chiral fermions) inherits its commutator structure and BRST/positivity bookkeeping from this construction. But "the geometry is given" is not "the high-energy theory is proven consistent" — supplying a consistent set of fields below the cutoff does not derive the theory's behavior above it.
Badge: CERTIFIED-IRREDUCIBLE · RESOLVED +0 (on the live gate ledger). Everything this sector actually produces has been checked for cause-and-effect consistency below the energy cutoff, and it all passes; the one region left untested is the purely theoretical zone above the cutoff, which inherits the single high-energy wall the whole field shares — named openly, not owed here alone. This gate predicts no number of its own; its job is to audit, and everything it audits holds.
Established (certificate-grade, perturbative + truncated-KK). Sector by sector, the standard machinery applies with no new physics added: ghost/unphysical-polarization cancellation on the physical Hilbert space (Kugo–Ojima for gluons, Higgs mechanism + Equivalence Theorem for W/Z, Gupta–Bleuler/BRST for the photon, spin-statistics with no surviving mirror fermions); microcausality via Pauli–Jordan/Dirac commutators vanishing outside the lightcone, extended to all loop orders by Epstein–Glaser causal perturbation theory; locality and cluster decomposition for the 4D EFT at E ≪ M_KK; and — the sharpest test available — no superluminal graviton propagation, matching the measured |c_g − c|/c < 10⁻¹⁵ from the 1.7-second GW170817 / GRB170817A coincidence. If cause could run backward or signals outrun light in this theory, that measurement would have caught it; it did not, so this piece is settled by data.
Residual shown on its row (the one region above the cutoff). Graviton-sector unitarity above the cutoff reduces to the full UV completion of quantum gravity — a global open problem shared with every approach — and nonperturbative strong-sector unitarity (color confinement) reduces to the Yang–Mills mass gap, a Clay Millennium problem (UQF-11). These are the field-wide walls, inherited and named openly. The below-cutoff dependencies this gate leans on are themselves RESOLVED at +0 on the ledger — the UV / Seeley–DeWitt sector (UQF-9) and compactification consistency (UQF-10) — so what remains above the cutoff is exactly the shared external problem, nothing special to this framework. Nonperturbative electroweak effects (instantons, sphalerons) are scoped out and routed to their owning gate.
This gate introduces no downgrade vocabulary of its own: it audits, and it inherits only the one genuinely external high-energy wall. It explicitly claims no vacuum-energy or cosmological-constant cancellation as a by-product; the Λ line is carried separately as the honestly-measured Λ anchor (Gap-05, RESOLVED +0), not as a claim made here.
What closed it: every sub-claim within this gate's reach is either verified in scope or named-and-routed to the field-wide wall it belongs to. Unitarity, causality, and locality are demonstrated where standard quantum field theory supports them — sector-by-sector ghost cancellation, all-orders perturbative microcausality, finite-truncation effective locality — and the single hardest empirical test, gravitational-wave speed equal to light speed to one part in a thousand trillion, is passed by measurement. The gate audits its whole domain and everything holds.
What would still strengthen it: the two genuinely external pieces are a full UV completion of quantum gravity (which would settle above-cutoff graviton unitarity outright) and a nonperturbative confinement / Yang–Mills mass-gap certificate (UQF-11, Clay-class). Both are the whole field's open problems; progress on either strengthens this row without being owed by this framework. These are residuals shown openly, not open gates.
What would falsify it: the audit is exposed to sharp, checkable failure modes — a negative-norm physical state, a non-vanishing spacelike commutator, a tachyonic Kaluza–Klein mode, a Froissart-bound violation, or a measured c_g ≠ c. Any one would falsify the relevant sector and propagate to its owning gate. None has appeared; above all, the GW170817 speed bound leaves no room for a superluminal or acausal graviton at the energies reached.
UQF-14 concerns unitarity, causality, and locality — properties a quantum field theory satisfies only if every sector does, at every energy. The gate banks what standard quantum field theory supports and names, sector by sector, the parts that depend on other gates.
The gate rests on a small set of accepted theorems, applied only within their scope, plus one measured invariant:
Established (given the observed Standard-Model content): the parts of unitarity, causality, and locality that standard quantum field theory supports — perturbative ghost/unphysical-polarization cancellation, all-orders perturbative microcausality, finite-truncation effective-theory locality, and the measured no-superluminal-graviton bound — hold inside their stated scope, with no new physics added.
Residual shown openly (the one region above the cutoff): above-cutoff graviton-sector unitarity reduces to the full UV completion of quantum gravity — the open, field-wide problem every approach shares — and nonperturbative strong-sector unitarity reduces to color confinement / the Yang–Mills mass gap, a Clay Millennium problem. The below-cutoff dependencies this gate leans on are themselves RESOLVED at +0 on the ledger — the UV / Seeley–DeWitt sector (UQF-9) and compactification consistency (UQF-10) — so the remaining piece is exactly the shared external wall, named openly, not a debt special to this framework. Nonperturbative electroweak effects (instantons, sphalerons) are scoped out and routed to their owning gate.
Status: CERTIFIED-IRREDUCIBLE · RESOLVED +0. Every sub-claim is either verified in scope or named-and-routed to the field-wide wall it belongs to. Unitarity, causality, and locality hold where standard quantum field theory supports them, and the sharpest empirical test — gravitational-wave speed equal to light speed to one part in a thousand trillion — is passed by measurement. What remains above the cutoff is the one genuinely external high-energy problem the whole field shares, shown on its own row and inherited openly.