Source and dependency ledger

Checked 8 September 2026. External novelty and priority of the present synthesis are unassessed.

Actual datum: formal external dependency

Tudor Dimofte and Stavros Garoufalidis, The quantum content of the gluing equations, arXiv:1202.6268v2, 25 October 2012.

• Section 2.6: the two labeled tetrahedra, both complete edge rows, and the meridian row.
• Section 4.6: the canonical longitude row -2Z+2Z’=2v, and the distinction between that raw combinatorial holonomy and the SL2 lift ell=-exp(v).

The current note takes this fixed actual incidence datum as input. It does not attribute its newly derived cone, phase, or vacuum conclusion to Dimofte and Garoufalidis. Their geometric eigenvalue conventions are not imported in place of the retained native quantum scalar dictionary.

Retained FPRD proof dependencies

• One-sided seed and exact cone theorem: the single required recurrence, all-input summability, and original-sided full-image descent.
• Native local collar comparison: the exact six-root named-action dictionary at generic parameter, based on Panitch–Park, Garoufalidis–Yu, and Chen–Kricker. Its references and exact scope remain in force.
• Generic filling reconstruction: the identification of the filled vacuum with 1-l^2 in the native meridian cokernel, using the boundary module reconstruction sources credited there.
• Actual incidence and native raw scalars: P(R)=(r-s;t-s), B^(prime sum), and the earlier two-angle result.

These are retained AI-assisted research dependencies, not external validation of this note.

Intellectual influences distinguished from new claims

• Euler’s quantum-dilogarithm coefficient expansion, recorded in DLMF 17.5.1, supplies the classical local coefficients. No new special function is claimed.
• Stavros Garoufalidis, The 3D index of an ideal triangulation and angle structures, supplies the ordinary tetrahedron index used in the failed-ray comparison. Its extra recurrence is not imposed on the one-sided seed.
• Garoufalidis–Hodgson–Hoffman–Rubinstein’s normal-surface interpretation influenced the previous angle/index strategy. Their boundary inversion theorem is not a formal dependency of the new opposite-sign argument.
• The idea of pairing a quantum relation module with a local difference-equation solution precedes this note. The present work supplies a specific alternative sign certificate and its actual-data application, with novelty unassessed.

External problem scope

Panitch–Romo, arXiv:2609.02706v1, Section 7, Conjecture 7.1 asks for the nontrivial Dehn-filled quantum-trace quotient for arbitrary ideally triangulated oriented 3-manifolds and chosen fillings. Its statement was checked in the retained primary-source text. The restricted family here is not a resolution. No author contact is warranted by this supporting note.