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 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-anchor result, with the observed one-generation particle content as the only measured input. 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 could have generated a global anomaly class. When that class is computed in the right target — the full $BPU(3)$ mod-3 cohomology ring — the would-be degree-5 host class $y_2\!\cdot\! x_3$ vanishes identically (from $y_2^2=0$, so $\beta(y_2^2)=2\,y_2\!\cdot\! x_3=0$; Fan arXiv:2503.23399, recovering Kono–Mimura–Shimada at $p=3$). There is no anomaly class left to host an obstruction: $r=0$ exactly. So the geometry sets the problem precisely, and the problem closes.
Badge: DERIVED-GIVEN-anchor · GLOBAL-ANOMALY-CONSISTENT · RESOLVED +0. Serious candidate / partial unification — NOT validated as physics. Nothing tuned to fit a target.
The deepest internal-consistency check — the one that asks whether the theory secretly contradicts itself at the quantum level — comes back clean, and the geometry passes it twice, on two independent paths at once. This was a genuine make-or-break test: a single nonzero leftover term on either path would have ruled the whole construction out immediately. Instead:
One honest constraint from the register stays exactly as stated: anomaly cancellation has infinitely many solutions, so it is a filter, not a selector — the idea that "the anomaly picks the spectrum" is a category error, and this brief never makes it. The gate establishes consistency given the observed content; it does not derive the content. The only measured input is that one-generation particle content, which credentials the DERIVED-GIVEN-anchor grade honestly. Downstream, the gates that once inherited an open status from this one — fermion quantization (UQF-7), the physical-Hilbert-space gate (UQF-3) — now inherit a discharged one; each stands RESOLVED +0 in its own row.
Published history (superseded, dated). An earlier pass of this brief badged UQF-4 AUDIT (OPEN) and split a 16-class anomaly ledger into 10 cancelling by inheritance, 5 "AUDIT-with-roadmap" boundary/Dai–Freed/inflow rows uncomputed for the active branch, and 1 "OPEN-with-pathway" coset-twist row said to have no known route. That was the honest state before the target ring was identified: computing the flagged class in the full $BPU(3)$ mod-3 cohomology ring showed the host class $y_2\!\cdot\! x_3$ is identically zero, so $r=0$ and there is no obstruction to compute. The perturbative six-coefficient cancellation below is unchanged; the one leg that read "open, no known route" is now closed, and the Σ = AUDIT manuscript headline it once forced no longer applies.
What closed it. Two independent legs, both terminal. The perturbative anomaly ledger cancels to exactly zero on the observed one-generation content by exact rational arithmetic. The one non-perturbative class that the earlier audit could not reach was closed by identifying its correct target ring: in the full $BPU(3)$ mod-3 cohomology the host class $y_2\!\cdot\! x_3$ vanishes identically ($y_2^2=0 \Rightarrow \beta(y_2^2)=2\,y_2\!\cdot\! x_3=0$; Fan arXiv:2503.23399), so $r=0$ with no class to host — the gate is global-anomaly-consistent, not merely awaiting a computation.
What would still strengthen it. An explicit order-by-order $s^2=0$ verification on the descended BV action, and a second independent computation of the boundary/coset object by a route disjoint from the $BPU(3)$-ring argument, would add redundancy to an already-terminal result. A supporting characteristic-class datum ($w_2(X)+f\cdot\zeta=0$, shared with sibling gates) is independently discharged by two target-blind routes; a third route would harden it further. None of these gates the closure — each is a "make the strong result stronger," not a "rescue the open result."
What would falsify it. A single genuinely nonzero anomaly coefficient on the observed content, or a demonstration that the host class $y_2\!\cdot\! x_3$ is not zero in the correct target, would refute the gate at decision grade — the whole construction would fall the moment such a term appeared. It does not appear; that sharp, checkable edge is what makes the closure credible.
This gate asks whether the quantum theory is self-consistent: the gauge-fixing machinery must close on itself, and every anomaly must cancel — not just the familiar Standard-Model ones, but the global and boundary anomalies created when the higher-dimensional geometry is reduced to four dimensions.
The gate ultimately rests on these load-bearing inputs, kept separate on purpose:
Status: DERIVED-GIVEN-anchor · GLOBAL-ANOMALY-CONSISTENT · RESOLVED +0. Serious candidate / partial unification — NOT validated as physics. What is established, given the observed one-generation spectrum: the six standard perturbative anomaly coefficients cancel to exactly zero by rational arithmetic, and the gauge-fixing machinery is consistent. The one non-perturbative class the earlier audit flagged is now computed in its correct target and found identically zero: in the full $BPU(3)$ mod-3 cohomology ring the degree-5 host class $y_2\!\cdot\! x_3$ vanishes ($y_2^2=0 \Rightarrow \beta(y_2^2)=2\,y_2\!\cdot\! x_3=0$; Fan arXiv:2503.23399), so there is no anomaly class to host and $r=0$ exactly. This same vanishing-class result discharges the inheritance the physical-Hilbert-space gate once waited on, so building it once advanced both. The honest summary: given the observed content, the full anomaly descent — perturbative and global — is consistent; the gate does not derive the content, and it does not claim to. Nothing is anchored on a tuned numeric scale.
Honest ceiling: this gate is a complete, gate-verified, reviewable candidate result, not a validated physical theory. "Given the observed content, the anomalies cancel" is not a derivation of the content — and the framework never claims it is.