Hostile audit — global meridian-index detector

8 September 2026. Internal audit of the companion ATTACK note, not external expert review. Verdict: a conditional global nonvanishing theorem with an explicit construction-specific obstruction; not a Publication or an unrestricted filling theorem.

The central claim survived these checks

The functional is defined on the original native algebraic target, including every actual moment row and all root parities. Under exact character consistency, nonnegative filling-angle feasibility and the no-null-ray condition, the proof shows order-independent convergence on every input and value $1+$ positive order on the cokernel unit. Each hypothesis is used explicitly. None is asserted to hold for every actual filling.

Presentation and conventions

1. Are the two sides reversed? No. Native tetrahedron relations are $Sf_j$, so the seed must annihilate right multiplication by $f_j$. Moment relations are $(c_jW(h_j)+A^2)S$, so averaging imposes a left eigencharacter. Equations (20), (36), and (37) check the actual sides. A CK-sided presentation must first pass through the retained comparison; it cannot be substituted directly.

2. Does the index use the right parameter? Yes: $q=A^4$, $q^{1/2}=A^2$, and root Weyl multiplication has exponent $\Omega_2/2$. Thus $W(u)z^{-2}$ has coefficient $A^{-u_w}$, not $A^{u_w}$. The choice $I_\Delta(u_w/2,-u_z/2)$ gives exactly the sourced first recurrence. The verifier checks this translation and a cleared-denominator telescoper. The all-integer recurrence remains a cited theorem, not an inference from the finite series check.

3. Were opposite roots identified? Only an ordinary projection to one central sign sector is used. The scalar $\sigma^b(iA)^s$ in equation (8) is retained in every moment. A nonzero sector quotient proves the full target nonzero, without inverting that projection. There is no assertion that every sector survives.

4. Were dependent edges discarded? No. The character is prescribed on every actual edge and the actual meridian, and must respect all integer dependencies. Its scalar phases matter, not just its valuation. The averaging runs over the image lattice of all rows, counting a lattice element once. Summing over redundant generator coordinates would create an artificial infinite multiplicity.

5. Was the moment lattice saturated or squared? No. The functional averages over exactly $\Lambda$. The auxiliary $\Lambda_0=\Lambda\cap2L$ describes the terms that contribute to a given even-supported seed; it is not a replacement moment lattice. For an arbitrary root input, the contributing terms form either an empty set or an affine coset of $\Lambda_0$. Reindexing the full $\Lambda$ proves the eigenrelation for odd as well as even moments.

Convergence and nonvanishing

6. Was convergence proved only on (1)? No. The input-dependent phase in (29) could be negative and unbounded if treated alone. For every affine input, Dickson’s lemma supplies finitely many minimal $b$. The difference $F=x-b$ lies in the homogeneous nonnegative cone. Isotropy transforms the dangerous phase into $2(2\delta-\Omega_3)(b,F)\geq0$. Equation (33), followed by compactness in (34)–(35), gives a uniform degree bound for that input. The symbolic verifier confirms the exact residual is precisely the moment isotropy pairing.

7. Could infinitely many moment labels have one reduced representative? No. The middle coordinate of each block of $T(v)$ is zero. A difference $T(v-v')$ equal to a tetrahedron translation must therefore have zero translation coefficient, and then $v=v'$. This makes the degree bound a bound on summands, not merely on a quotient of labels.

8. Does a weak angle certificate suffice without hidden strictness? Yes, with (16). On the compact unit section of the homogeneous cone, $\delta+\theta\cdot{}$ is positive because both terms are nonnegative and have no common nonzero zero. Homogeneity gives a linear lower bound on integral cone points. The one-block lattice model in Section 7 has no strict certificate but satisfies (16); it is explicitly not a triangulation realization.

9. Can leading coefficients cancel away the detected unit? No. The zero lattice element contributes constant coefficient (1). Every other contributing summand has strictly positive valuation. This does not require positivity of its coefficient, and root-of-unity phases in $\chi$ are harmless for this single leading coefficient. The resulting field-valued functional on the original finite Laurent domain proves algebraic target nonvanishing.

10. Is a new completion-created class being detected? No. The source is $S$, not a shape-local completion of $S$. Rational coefficient functions embed in $K=\mathbb Q(i)((A^{1/2}))$. Sending the original algebraic class (1) to a nonzero element of $K$ is sufficient. Nothing is inferred from the dimension of a completed quotient. The $A=0$ coefficient expansion does not contradict the earlier $A=e^\hbar$, point-local clean-excess obstruction.

Exact failure boundary

11. Does a real null ray really yield an integral one in the unsaturated lattice? Yes. Restrict to the support of a nonnegative null vector. On that support, the skew-lattice equations and the angle-zero equation are rational linear equations; $\delta=0$ is automatic because there is at most one nonzero coordinate in each block. There is a nonzero rational point with that support. After clearing denominators, a further integer multiple lies in $H$, which has finite index in its saturation in its rational span. Its reduced representative determines a nonzero $\mu\in\Lambda_0$. All positive multiples have nonzero summands of valuation zero. This rules out the unordered average, not all regularizations or all functionals.

12. Can cancellation rescue the same definition? Not as an unordered $A$-adic sum. Such a family must have only finitely many terms at each bounded degree. An infinite zero-degree family fails that criterion regardless of signs. A contour prescription, analytic continuation, or regrouping would be a different construction requiring its own descent and nonzero-value proofs.

13. Is the finite-density obstruction too broad? The proved statement is limited to a separating constant-term pairing with a density in a domain. Finite Laurent densities satisfy it and cannot work. Rational residues with boundary jumps need not satisfy those hypotheses. The note does not rule them out. The successful functional is in the algebraic dual, not an ordinary Laurent-domain density.

What is still missing

14. Does the theorem prove a nonzero descended trace? No. The intrinsic filling isomorphism sends the filled vacuum to $1-l^2$. The note isolates $\mathcal F(1)-c_l^2\mathcal F(W(2b))$, and the second term can have a different minimum degree or cancel the first. No nonvanishing result for that difference is claimed. A nonzero abstract target is not a nonzero map from the filled skein module.

15. Is this independent of known index theorems or a new surgery invariant? No such claim is made. DGG, Garoufalidis, GHHR, and GY supply the seed, symmetries/degree, and lattice-sum method. GY’s all-input even-target construction is a particularly close dependency. Celoria–Hodgson–Rubinstein already prove a rigorous surgery formula under their hypotheses; the current v2 theorem was checked. No equality with that invariant, cycle pairing, or triangulation-independent invariant is proved here.

16. Does this demonstrably enlarge the actual geometric class? It removes the classical-shape and intersection assumptions from the theorem statement and allows a weak-angle certificate. It does not demonstrate that a chosen actual triangulation/filling outside the earlier chamber satisfies the certificate. The only strict-versus-weak separation supplied is an abstract lattice model. No topological census or configuration search was performed.

Rejected shortcuts retained for the next attempt

Do not use a finite summation box as proof of a reindexing identity. Do not extend the seed by zero and then check only even moments. Do not impose an arbitrary character on a convenient basis without its actual dependent-row phases. Do not invoke an unfilled angle structure while omitting the affine meridian equation. Do not use (1) in place of $1-l^2$ when claiming trace nonvanishing. Do not infer actual target vanishing from a divergent index or a zero formal-local detector.

Publication significance and recommendation

The outcome is useful: it supplies an explicit global adjoint solution for the actual mixed-sided meridian presentation and identifies a sharp weak-angle obstruction to this particular construction. Its mathematical scope is conditional and target-level. A Publication recommendation would require additional priority assessment and specialist review, together with a clear case for significance relative to the close existing index literature. The recommended next mode is ATTACK on the longitude difference or on a new detector at the null-ray boundary.