Hostile internal audit: native six-root peripheral lift

8 September 2026. Internal adversarial audit, not independent human expert review.

Retained first checkpoint audit. Its open-gate verdict is historical. The current continuation is audited separately in local-collar-hostile-audit.md.

Verdict

The native generic six-root peripheral extension survives the checks below, with its source dependencies explicitly retained. The raw CK/PP named-action transport remains unproved. This is a research note. Do not promote it to PUBLISH or claim Panitch-Romo 7.1.

1. Did the proof invert an opposite-root quotient?

No. It defines the full native GY module first, with the six actual bare-edge labels. The local standard-off-diagonal quotient and the corner-reduced skein module both precede opposite-root identification in GY’s construction. The extension tracks identities at those earlier stages. Its plus-sector image is a check, not its proof.

The earlier local nonzero minus-sector result is preserved. We do not infer that every global sector survives an edge quotient.

2. Does the source two-state calculation secretly equate opposite arcs?

The vulnerable replacement is GYI Lemma A.3. It replaces a substandard arc by its parallel standard arc, with reversed state, modulo standard off-diagonal terms. The parallel arc lies at the same bare edge. That lemma is in the corner-reduced lantern module, not the three-root quotient. The off-diagonal terms vanish already in the full GY local target, as presented in GY Theorem 4.25.

The later commutation/Weyl claims are claims about lantern arcs before root identification. The six-root skew form is the pullback of the collapsed form; this is an exact matrix identity, not an appeal to equality of quotient elements.

The proof imports GY’s admissible-diagram construction and local claims rather than independently re-proving their geometric setup. A defect in one of those source inputs would affect this extension. This dependency is not described as a new independent proof of the source theorem.

3. Was the action checked only on the empty skein?

No. Proposition 3.1 carries an arbitrary additional skein through the source state-annihilation and standardization argument. The two-generator lemma requires the two insertion identities on every input. A scalar or vacuum trace computation would not meet that hypothesis.

4. Are peripheral operators defined on the full target?

Yes in the native GY presentation. Left multiplication preserves the left-generated tetrahedron relation module. Pairing zero with every actual edge row makes it preserve the right-generated edge relation module. Pairing zero follows from the collapsed NZ rows and the exact pullback identity for the six-root form. Invertibility follows by applying the same argument to the negative row.

The proof never uses a full ambient half-edge algebra action, nor assumes tetrahedron polynomials are two-sided relations.

5. Did the sum-of-slopes construction merely choose an arbitrary lift?

Its exponent vector is chosen additively, but its named insertion identity is proved, not assumed. At generic parameter the skein commutator expresses the actual third generator in the first two. Their two operator identities therefore force the third. All remaining torus skeins follow from the source three-generator theorem.

No claim is made that a separately drawn normal representative has a literally additive unquotiented exponent vector. The equality asserted is the desired action through the trace. The operator family itself is defined on the full target. No surjectivity of the trace is used to conclude equality on the full target for different geometric choices.

6. Are generic denominators disclosed?

Yes. The step uses the inverse of A^2-A-2. It proves no integral or root-of-unity extension at A^4=1. The local two-state calculation itself does not require that inverse, but the additive all-slope conclusion in this packet does. The coefficient field is fixed at the outset.

7. Were central signs lost in Weyl ordering?

No. The local elimination formula contains sigma_T raised to the full opposite-exponent sum. That sum is an additive integer functional. The sum-slope sign is the product of the two basis signs. Weyl ordering contributes A^-pq in the ordered GY basis with B(lambda,mu)=2.

The inverse of A^-1 LM is A^-1 L^-1 M^-1. Using A L^-1 M^-1 would be wrong. The verifier checks the precise formula.

8. Was the Type II closing correction dropped?

No. GYI’s annulus counit supplies q^-1/4=A-1, compensated by the uncancelled height-order contribution. It is a prequotient counit calculation. The annular buffer contributes no shape root. This detail is stated separately because treating the two types identically without it would leave a quantum factor error.

9. Did an algebra anti-isomorphism get advertised as a named-trace comparison?

No. The fixed-parameter prime-reversal map and the conjugate inverse-root map are proved as algebraic presentation maps only. The paper states exactly what must still be checked to make one the actual collar convention map.

The naive fixed-parameter inverse-root anti-map fails before quotienting. This gives a useful countercheck against treating root inversion, state reversal, coefficient conjugation and product reversal as interchangeable words.

10. Are the raw state and ribbon conventions really finished?

No. Diagonal standard-arc values and local shape relations determine an algebraically viable map. They do not determine the mixed-state duality coefficients or establish compatibility with gluing. The GY and symmetric CK/PP cup diagrams have coefficients differing by the half-twist i A^(3/2). This scalar is verified, but the full geometric implementation and paired-cut cancellation are not.

It would be incorrect to use the present native theorem to claim the original PP six-root peripheral action. That remains the next decisive local question.

11. Is there genuine underdetermination after quotient comparison?

Yes. Multiplying an additive peripheral family by a central sigma-valued character preserves its quantum-torus law and disappears after opposite-root identification. It need not preserve the named trace. This is an exact obstruction to inferring a named lift from algebraic and identified data alone. The ambiguity is in two basis values, not an independent sign on every slope.

12. Does the computation certify the geometry?

No. It certifies the universal skew-form identities, the fixed local Weyl and commutator calculations, ideal witnesses for the algebraic anti-maps, and cup scalar ratios. It explicitly excludes the geometric source lemmas and the unresolved collar square. It performs no configuration search.

13. What is the magnitude?

Useful internal progress: an actual source-native named action replaces an unproved six-root lift, and an artificial third-sign gate is removed at generic parameter. Most of the argument is a careful extension of GY’s published/preprint proof. It is not a major boundary move, not a new nonvanishing theorem, and not a solution of PR 7.1. External novelty remains unknown.