# UQF-4 — BRST / Anomaly Descent

## What this gate must establish

Quantizing the framework's four-dimensional physics requires the gauge-fixing machinery (BV–BRST) to remain self-consistent and *all* anomalies to cancel — not only the familiar perturbative Standard-Model anomalies, but the global and boundary anomalies that appear when the higher-dimensional geometry is reduced ("descended") to 4D. Concretely, the gate demands two certificates: that the BRST operation squares to zero order-by-order ($s^2=0$ on the BV action), and that every anomaly polynomial vanishes on the physical Hilbert space after the descent and after a fixed regulator choice. If either fails, the quantum theory is inconsistent.

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

The frozen 13D geometry (active branch on $K_6\times S^2\times S^1$) supplies the matter content, the symmetry group, and the descent map; the perturbative anomaly ledger then cancels *given that content* — a DERIVED-GIVEN-E result, not an independent derivation of the content. The geometry is load-bearing in a sharper way for the hard part: the boundary structure ($S^1/\mathbb Z_2$), the bulk/boundary inflow, and the coset twist of $K_6=SU(3)/T^2$ are exactly what generate the anomaly classes that have *not* been computed in any prior work. So the geometry sets the problem precisely; it does not, by itself, certify that the problem closes.

## Current honest status

**Badge: AUDIT (OPEN). Serious candidate / partial unification — NOT validated. No status was ever upgraded.**

The corpus splits the 16-class anomaly ledger honestly:

- **10 of 16 classes — CERTIFICATE by inheritance.** The standard SM cubic and mixed anomalies ($SU(3)^3$, $SU(2)$-Witten, $U(1)^3$, gauge–gravity) cancel by inheritance from the 4D ledger plus textbook even/odd-dimension rules. This is the "perturbative anomaly ledgers vanish" claim — and it is given the spectrum, not a prediction of it.
- **5 of 16 classes — AUDIT-with-roadmap.** The $S^1/\mathbb Z_2$ boundary rows, Dai–Freed / Freed–Hopkins global rows on the boundary and on $K_6\times S^2$, and the bulk–boundary inflow row require a calculation whose machinery is well-defined (Hořava–Witten, Dai–Freed, Cordova–Ohmori) but which has **not been performed for the active branch**.
- **1 of 16 — OPEN-with-pathway: the coset-twist anomaly (row 17).** The non-perturbative coset-twist / BV–BRST descent anomaly has **no known route**. The pathway is named and the failure mode is sharply specifiable, but no construction exists in any prior work.

Two further honest constraints from the register: anomaly cancellation has infinitely many solutions, so it is a *filter*, not a selector — the idea that "the anomaly picks the spectrum" is explicitly dissolved as a category error. And only about 10 of 16 quantum-consistency classes currently close. Downstream, this AUDIT status is contagious: the fermion-quantization (UQF-7) and gauge-boson (UQF-6) rows downgrade one tier each, the physical-Hilbert row (UQF-3) loses its certificate, and the paper as a whole cannot exceed AUDIT until UQF-4 closes.

## What would close it

A two-part construction: (1) verify $s^2=0$ order-by-order on the BV action for the descended theory, and (2) explicitly compute the 5 AUDIT boundary/Dai–Freed/inflow rows for the active branch and resolve the OPEN coset-twist row. The first four are textbook-machinery calculations with a named Year 0–2 roadmap. The fifth — the non-perturbative coset-twist anomaly — is the genuine no-go: it has no known route today and is the binding blocker. A specialist construction that builds the coset-twist descent anomaly explicitly, with its inflow term, is what would move this gate off AUDIT. Until then the honest endpoint is: classical and retained-sector BRST nilpotency hold, the perturbative ledger cancels given the spectrum, and the full non-perturbative descent is unverified.

## Sources

- Quantum Paper III, main manuscript §5.4 ("BV/BRST nilpotency and anomaly closure (UQF-4)") — gate card, 16-class accounting, downstream downgrade map. Published at https://physics.magflowmeters.com/articles/Quantum.html
- Quantum Paper III, Appendix U (formal authority), card U1.3.4 — verbatim tier, pass/fail rule, falsifier, frozen inputs, artifacts U05/U08.
- Gaps & Walls Register, rows UQF-4 and SG-4 (hypercharge / anomaly cancellation) — the "filter not selector" dissolution and the "no known route" statement for the coset-twist / BV–BRST descent.

*Honest ceiling: this gate is a serious, sharply-specified audit state, not a validated result. "Given the spectrum, the perturbative anomalies cancel" is not a derivation of the spectrum, and the non-perturbative descent remains open.*