Hostile internal audit: clean-excess meridian detectors

8 September 2026. Internal adversarial review, not independent human specialist review.

Verdict

The proof supports a conditional theorem about formal-local quotients of the actual six-root relation system, and two exact algebraic obstruction models. It does not establish unrestricted nonvanishing or vanishing of the actual meridian cokernel. This is a supporting research note, not a Publication. PR 7.1 remains open in this work.

1. Did the target silently change?

No. The starting object is the inherited generic native six-root meridian cokernel. Vertex elimination and central idempotents expose its sign sectors without identifying opposite roots. The displayed formal object is explicitly a candidate detector for that algebraic quotient, not a replacement definition of filling.

The named peripheral action, generic cokernel isomorphism, and CK/PP comparison are inherited dependencies. This note does not re-prove their diagrammatics, remove their parameter restrictions, or establish new canonicity.

2. Are the sides correct?

Yes. A relation subspace $Sf_i$ is the image of right multiplication by $f_i$; $g_jS$ is the image of left multiplication by $g_j$. Distinct tetrahedron functions commute. The independent edge/filling monomials commute. Left and right multiplication commute by associativity. This exact commuting family defines the deformed Koszul complex.

The sign in the derivative formula follows from opposite sides: the two half-Poisson terms add after applying the classical syzygy. Putting both relation blocks on the same side would give a different calculation and need not define a complex.

3. Is a nonzero special fiber being mistaken for a generic one?

No. The main theorem proves the opposite: in its clean-excess situation the entire formal-local quotient is killed by $\hbar$, despite its nonzero classical fiber. The algebraic cyclic model separately has identical nonzero classical filling fibers for two quantizations with different generic cokernels.

4. Is the Bockstein really well-defined?

Yes. A classical syzygy has deformed image divisible by $\hbar$. Changing its lifts changes the quotient after division only by an element of the classical ideal. A classical Koszul boundary can be lifted using the exact commuting operators, making its deformed image exactly zero. Thus the obstruction descends to classical $H_1$.

It is only $\mathbb C$-linear. Formula (8) explicitly exhibits its failure to be $R/I$-linear. Multiplication on Koszul homology does factor through $R/I$, because each generator is null-homotopic by wedge multiplication. The derivative term is tangent to that quotient.

5. Does first-order surjectivity justify all orders?

The proof supplies the missing argument. Given any $w$, a first-obstruction preimage produces $dv=\hbar w$ modulo $\hbar^2$, after removing an ordinary boundary. Repeated corrections, weighted by successively higher powers of $\hbar$, converge in the finite product $W^{N+k_0}$. Applying the continuous finite operator sum gives exact equality.

This proves $\hbar W\subset\operatorname{im}d$, not merely that the unit is killed at finite precision. It does not assume the operator image is closed. It uses completeness of the coefficient-vector domain, and the limit is one vector with finitely many formal-series entries. The same step is not asserted for finite Laurent polynomials.

6. Is deficient Jacobian rank enough?

No. The theorem assumes a smooth scheme-theoretic common locus of excess dimension. This makes actual relation dependencies available with coefficients nonzero at the point. A singular complete intersection may have deficient Jacobian and still be a regular sequence. Smooth reduced support with embedded nilpotents also does not satisfy the theorem’s hypothesis.

Both separate blocks must have independent differentials. If that fails, a syzygy could live entirely inside one block, and its mixed Hamiltonian vector need not be nonzero. For actual invertible tetrahedron shapes and independent moment rows, the separate-block condition is automatic.

7. Why is the tangent operator surjective?

A syzygy nonzero at the point gives a nonzero conormal in each independent block. The ambient shape Poisson form is nondegenerate after vertex elimination, so the corresponding tangent vector is nonzero. In a smooth formal coordinate ring it has a unit coefficient in one direction. Dividing by that unit reduces the equation to an inhomogeneous first-order formal evolution equation. Coefficients are solved recursively by dividing by $n+1$, valid in characteristic zero. This does not require analytic convergence or a claim about global primitives.

Every quantum scalar contributes only a zero-order term. Such a term does not spoil formal solvability when the derivative coefficient is a unit. Thus the argument retains, rather than guesses or discards, the actual $A$-dependent moment scalars.

8. Are extra edges or sign sectors being discarded?

The obstruction is first proved using a selected independent edge/filling subset. The full local quotient has more relations, so is a further quotient and is also killed by $\hbar$. No equality between independent-edge and all-edge ideals in every sign sector is assumed.

The theorem is conditional at a point in a chosen central sign sector. It proves neither survival nor death of every algebraic sign sector. Finite central decomposition is bookkeeping; it is not a universal detection theorem.

9. Is the folded calculation an actual triangulation counterexample?

No. It retains exactly the tetrahedron polynomial form and an independent isotropic moment lattice, and exhibits the full local obstruction in closed form. Neither moment row is asserted to come from a manifold edge or actual filling curve. The explicit rational root point audits the algebraic witness only. The general theorem, not an unproved realization claim for this witness, is the application to actual targets.

The exact verifier checks the syzygy, Poisson signs, scalar corrections, Jacobian and formal recurrence. It does not turn the example into a topological construction.

10. Could all point-local detectors vanish while the global quotient survives?

Yes, and Section 5 proves it. The Laurent quantum-torus quotient has a nonzero Fourier coefficient functional, while formal logarithms at each intersection point supply primitives that kill its localized formal image. This is an explicit counterexample to treating these mixed-sided formal quotients as a faithful localization test.

The source map from the actual algebraic target to a completed detector is useful only when it sends some vector to a proved nonzero class. A zero detector is inconclusive about that source.

11. Does the cyclic resonance example test a weak or infinite-generation hypothesis?

The countermodel is already cyclic under the full peripheral quantum torus. It has an integral Laurent lattice, invertible $m,l$, the correct quantum commutation law, and nonempty classical filling support at $m=-1$. For $c=1$, every eigenvalue of $m+A^2$ is nonzero, and coefficientwise division is a legitimate inverse on finite Laurent sums. For $c=2$, exactly the constant monomial is resonant.

The model therefore refutes a universal deduction from those stated properties. It does not claim the model satisfies the full actual tetrahedron/gluing presentation. The vacuum distinction is explicitly retained.

12. Does existing deformation-quantization literature already cover the broad idea?

The broad derived-intersection and local-system picture is established literature. Gunningham–Safronov’s current primary text, especially Theorem 7.1 and Section 7.5, was inspected as a positioning check. It is not presented as a newly discovered phenomenon, and it is not applied without checking differences between formal power-series, sheaf-theoretic and algebraic Laurent categories.

The contribution here is the elementary first-obstruction calculation and exact extinction criterion for the specified mixed-sided presentation, plus explicit anti-inference models. Novelty and publication significance remain unassessed. No first-priority claim or specialist endorsement is made.

13. What remains safe to claim?

The actual question remains $\operatorname{coker}(m+A^2;Q_G^6)\ne0$. The previous regular-intersection and positive-geometric theorems still supply their conditional positive results. The new result blocks a naive extension of their formal-local proof through smooth excess loci. It recommends a global algebraic detector or a separately justified analysis of singular excess, with no census and no restart of peripheral signs.

The GY degenerate-chart warning is recorded only as a source-level caution. It is not upgraded to a new actual full-six-root/PP conjecture counterexample. No email or other author contact was made.