# UQF-14 — Unitarity / Causality / Locality

## What this gate must establish

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 geometry's role (load-bearing, not validation)

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.

## Current honest status

**Badge: AUDIT (OPEN). No status was ever upgraded.** Honest ceiling: a serious candidate offering partial unification — **not validated**.

The row splits into two tiers under the weakest-link rule:

- **Banked (certificate-tier, 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 no superluminal graviton propagation, consistent with |c_g − c|/c < 10⁻¹⁵ from GW170817 + GRB170817A.

- **Open (the blockers that set the badge).** Graviton-sector unitarity *above the cutoff* is conditional on **UQF-9** (UV completion), itself an AUDIT row and a global open problem shared with all of quantum gravity. Nonperturbative strong-sector unitarity (color confinement) inherits **UQF-11** (Yang–Mills mass gap, a Clay Millennium problem). Cluster decomposition with the full infinite KK tower inherits **UQF-10**. Nonperturbative electroweak effects (instantons, sphalerons) sit outside this paper's scope and inherit BG-10.

This gate introduces no downgrade vocabulary of its own: it **inherits failures**. If UQF-9 fails, the above-cutoff unitarity sub-claims fail with it. The gate explicitly claims **no** vacuum-energy or cosmological-constant cancellation as a by-product; the Λ line is recorded separately as a computed honest fail (Weinberg-open).

## What would close it

There is no self-contained closure path; the gate rises **only as its upstream dependencies rise**. Concretely: (1) a UV-completion certificate establishing above-cutoff graviton unitarity (closes the UQF-9 dependence); (2) a nonperturbative-QCD confinement / mass-gap certificate (closes UQF-11); (3) a compactification-stability certificate for the full KK tower (closes UQF-10). Until then, the honest statement is that unitarity/causality/locality are **demonstrated where standard QFT supports them and named-and-routed where nonperturbative subtlety enters** — structural discipline, not a deep nonperturbative proof. A negative-norm physical state, a non-vanishing spacelike commutator, a tachyonic KK mode, a Froissart-bound violation, or a measured c_g ≠ c would falsify the relevant sector and propagate to the owning gate.

## Sources

- Quantum Paper III (Q1 main manuscript), §17 "UQF-14 — Unitarity / Causality / Locality Audit," and the §2/§3 gate ladder. Public copy: https://physics.magflowmeters.com/articles/Quantum.html
- Formal per-sector inventory (negative-norm/ghost ledger; commutator-vanishing ledger; audit-status matrix): Q3 / Appendix U, module U-AUDIT-B.
- Gaps & Walls Register, row UQF-14 (status: AUDIT/OPEN; blocker: graviton-sector unitarity above the cutoff, blocked by UQF-9).
- Upstream dependencies: UQF-9 (UV completion), UQF-10 (compactification stability), UQF-11 (nonperturbative QCD / Yang–Mills mass gap).