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Resolution of Chen–Kricker Conjecture 5.27

FPRD-CK-T01

Six-root quantum-gluing comparison isomorphism

Exact statement

For the standard right-tetrahedron/left-edge Laurent presentation in Chen–Kricker Section 5, the six-root shape relation module is exactly the intersection of the ambient Panitch–Park relation module with the six-root shape torus: S∩Rambient=JS\cap\mathcal R_{\mathrm{ambient}}=J. Hence the Chen–Kricker comparison map is an isomorphism.

StatusProved and independently hostile-audited within FPRD Lab; no external review
External reviewNo external or specialist review is recorded; the proof has passed an independent hostile internal audit.

Context

Chen and Kricker constructed a surjection from their six-root quantum gluing module to the six-root image inside the extended Panitch–Park target and conjectured it was injective.

Definitions

  • U is the full face-cone quantum torus; S is its six-root shape subtorus.
  • The difference-of-paired-exponents grading has degree-zero component U_0=S.

Hypotheses and scope

  • The standard presentation extends tetrahedron relations on the right and edge relations on the left.
  • The shape algebra is Laurent, as in Chen–Kricker Remark 5.23 and equation (5.7).
  • The coefficient ring contains only the distinguished units stated in Theorem 1.1.

Proof or evidence

Exact right-unit normalization puts every ambient tetrahedron generator into the degree-zero extension of a six-root relation. The degree-zero S-bimodule projection then computes the full mixed-sided intersection and proves injectivity.

Full proof →

Verification notes

The proof was independently reconstructed and challenged against the complete relation list, sidedness, coefficient ring, self-gluings, opposite-root sectors and named-trace scope. Ordered-PBW and independent Weyl verifiers pass. The full audit is at /evidence/dehn-filled-quantum-trace/ck-publication-audit/hostile-publication-audit.md.

Limitations

  • Chen–Kricker Definition 5.7(i) contains one contradictory 'left ideal' phrase; no theorem is asserted for that altered closure and no author-confirmed erratum is claimed.
  • There is no external peer review or author endorsement.
  • A bounded search found no earlier resolution but does not establish first priority.
  • This comparison theorem does not prove Panitch–Romo Conjecture 7.1. The later supporting local-collar packet records the named six-root peripheral action at generic parameter.

Open work

Obtain external specialist review and monitor the source conjecture for revisions or an author-confirmed sidedness correction.