Internal audit: phase-free degree separation

8 September 2026. This is a self-audit of an AI-assisted supporting note, not independent specialist or peer review.

Mathematical checks

1. Actual datum and target. The raw rows are copied from the retained source-checked Dimofte–Garoufalidis datum. Both edges survive in the character check. The target is the mixed-sided native all-plus vector quotient, not a replacement algebra.
2. Sidedness. The seed annihilates arbitrary left multiples of the tetrahedron polynomial. Isotropic image reindexing gives the character needed for arbitrary right multiples of edge and filling constraints. The proof establishes convergence on every algebraic root input before reindexing.
3. No phase adjustment. The exact character is unchanged. At the odd-numerator control the filling character is iA, and supported odd roots genuinely retain imaginary coefficients. The verifier checks these rather than passing to squared variables only.
4. Weyl and scalar factors. The expansion includes Omega(lambda,2b)/2 and 2rho from c_l squared. The complete-square constant is zero only with the native scalar. The verifier separately confirms that deleting it leaves -2rho.
5. Uniform degree argument. Q=x1*x2+(4+p/q)(x1-x2)^2/8 is strictly positive on the nonnegative orthant minus zero for the claimed strict cone. The linear coefficients 1±1/q are nonnegative for every nonzero integer q, including negative q and |q|=1.
6. The zero-coordinate case is not skipped. Strict copositivity alone does not exclude a=0. Its second seed coordinate is exactly (1/(2q),-1/(2q)), hence nonintegral. Merely showing 2b is not in the moment image would not suffice: the seed can be nonzero on nontrivial pure-w monomials.
7. Integral supports retained. No saturation of Lambda, replacement of the even-root seed support, or assumed image-surjectivity is used. The calculation proves a degree bound on a superset and then tests the only endpoint against the actual integral support.
8. Every complement. The generic symbolic identities impose only qr-pt=1 and q nonzero. They do not choose a favorable longitude sign. The native commutator orientation is Omega(h_s,b)=2.
9. Formal sums, not analytic rearrangements. Quadratic coercivity makes each coefficient a finite sum. Reciprocal finite Pochhammer factors have no negative powers. A unit constant one cannot be cancelled by any longitude term.
10. What positivity means. Positive order is not positive coefficient. An initially attempted diagnostic demanded a negative coefficient in the aggregated odd-numerator unit series; that was not implied by failure of the termwise sign certificate. It was replaced by the exact negative-summand witness 4h+2h_s. The all-orders proof never used the rejected diagnostic.
11. Generic target conclusion. The functional into the Laurent-series field detects the k-linear class. The filled vacuum is 1-l², not the unit. Its nonzero all-plus image implies a nonzero preimage in the original six-root quotient, conditional on the retained exact named-action/filling identification; no sector-projection injectivity is claimed.

Evidence and unresolved limits

The standard-library verifier establishes generic Laurent polynomial identities and a single odd-numerator control with exact Gaussian integer coefficients. Its infinite-series cutoffs have a displayed quadratic tail bound. These checks supplement, rather than replace, the symbolic proof.

The previously restricted sign theorem is preserved. Its phase criterion remains correct; its use as a necessary gate for this detector’s vacuum was too strong. No new seed is needed inside the present convergence cone.

The theorem does not cover q=0 or p/q≤-4 using this seed. The retained necessity result rules out this seed’s all-input unordered average there, but says nothing about vacuum vanishing. No unrestricted conjecture resolution, new invariant, triangulation independence, external validation, or priority claim follows. Publication and author-outreach thresholds are not met.