Internal audit: local move defect

9 September 2026. Same-agent audit, not independent confirmation.

Exact scope

The theorem concerns the local three-tetrahedron quotient with one interior edge, not an arbitrary globally glued triangulation. It computes a vector-space cokernel and its source-torus action. The source module itself is not an algebra.

Checked vulnerabilities

• Relation sides. Formula (4) consists of left tetrahedron multiples and a right edge multiple. The verifier checks it as an identity of sparse Laurent polynomials with exact symbolic q powers. The source image centralizes the edge, so arbitrary source left multiples are permitted.
• Weyl phase. The root factor iA squares to -A^2; Weyl-to-ordered conversion contributes A^2 for each of the four columns, giving -q, not -q^(1/2).
• Integral lattice. Formula (5) is an explicit integer inverse on the charge-zero kernel. No finite-index issue is hidden by working over the rationals.
• Resonance. Right ordering contributes q^(-c), followed by the edge eigenvalue q^(-1). The only vanishing coefficient is at c=-1. The coefficient would be wrong if right multiplication were treated as an action on the quotient.
• Spanning and independence. Positive charges reduce to zero; charges below -1 reduce to -1; a separate rational dual family proves independence. Formula (11) then follows by evaluating the dual basis, not by guessing an infinite expansion.
• Primitive sign. Formula (12) extends each functional to the primitive relation P=-A^2. Zero unsupported parity sectors are stable under both tested relation families.
• Finite inputs. Each H_s value is a finite rational expression. No convergence of an orbit average is inferred from this formula.
• No global counterexample. Exterior edge constraints are not yet imposed. The native F is not asserted to equal H_s, and nonzero local cokernel does not imply nonzero global cokernel.
• Directed transport. The global corollary uses the Garoufalidis-Yu preprint’s all-input identity in its stated direction, under 1-efficiency and the applicable homology condition. Both exceptional manifolds meet the latter. No path to every triangulation is claimed.
• Priority. The local move and general index compatibility are existing work. Novelty of the explicit resonant cokernel is unassessed. The source index paper is a preprint, distinct from the authors’ published quantum-trace paper.

Useful failure preserved

The proposed shortcut was: use an undirected 1-efficient move path and scalar or image-wise index invariance to transport any nonzero detector both ways. Formula (1) proves that the image can miss a whole explicitly described local summand. This rejects the inference; it does not reject a stronger global transport theorem with additional hypotheses.

Remaining gate

Impose the actual exterior relations on the affine Z^2 representation (13), and identify the native functional’s restriction there. An independent reconstruction of the local proof and of the native/GY all-input bridge is still required before independent-checking maturity credit.