Primary-source and priority ledger — longitude difference
Inspected 8 September 2026. No author contact, endorsement, or external specialist review is implied. No primary full texts are redistributed.
Fresh primary-source checks
| Source and pinned version | Inspected content | Role and boundary |
|---|---|---|
| Stavros Garoufalidis, The 3D index of an ideal triangulation and angle structures, arXiv:1208.1663v2 | Definition 3.1, Theorem 3.2, Section 4.5, Appendix B; abstract-page version history | Both tetrahedron recurrences, triality, and dimensions of the solution spaces. The abstract page identifies v2, revised 7 October 2015, as current. These are substantial prior ingredients, not new recurrences claimed by this packet. |
| Garoufalidis–Hodgson–Hoffman–Rubinstein, The 3D-index and normal surfaces, arXiv:1604.02688v1 | Section 2, equations (1)–(7), especially the leading coefficient; abstract-page version history | Exact symmetric index degree and sign. The q-degree is doubled to q^(1/2)-degree and then doubled again to A-degree because q=A^4. The abstract page lists v1 only. No topological realization is inferred from this formula. |
| Celoria–Hodgson–Rubinstein, The 3D index and Dehn filling, arXiv:2509.09886v2 | Section 6, surgery kernel and Theorem 6.2; Section 15; abstract-page version history | Current rigorous surgery prior art and its scope. The abstract page identifies v2, revised 19 December 2025, as current. No equality with the exact present pairing and no universal nonzero-value theorem is imported. Tables, census datasets, and implementation searches are not used. |
The tetrahedron index originates with Dimofte–Gaiotto–Gukov. The cited mathematical treatments provide the particular formulas used here. No first-construction claim for an index, a q-difference detector, or a Dehn-surgery index is made.
Retained, exact input packet
The newest completed mathematical state was confirmed to be the global-meridian-index release. The initial public renderer could not open the raw URLs, so the verified local copies were used initially. Subsequent direct read-only retrievals of both the live canonical handoff and active proof note succeeded: their SHA-256 hashes exactly equal the corresponding local-input hashes below. The owning workflow independently confirmed these were the newest completed inputs. No older stale automation text overrides those files.
| Retained input | SHA-256 of inspected local bytes |
|---|---|
global-meridian-index-attack/release/FPRD-global-meridian-index-detector-2026-09-08.md |
e2808966c6441b1dbf2fac5d6dfdb451ff299138a9061b56e14b348ce28d7195 |
canonical FPRD-research-loop-state.md |
d80b2a0525bb94cd2bc948c6d6122c11ab4ca3583267256f03f8bd4cab22909c |
six-root-peripheral-attack/release/FPRD-local-collar-square-2026-09-08.md |
96e79080bb4e78e2c669c1250ca4d93f5d0471b2d4bfd199717bda15e5597a59 |
The global note supplies the original all-input convergence/descent theorem and native reduced conventions. The six-root/collar packet supplies the retained exact named-action and scalar dictionary, including its CK source-reading caveat. The generic-boundary reconstruction’s Section 8 supplies the filling isomorphism and the distinction between the cokernel unit and the image 1-l^2 of the filled vacuum. The clean-excess packet’s earlier cyclic and Fourier witnesses were inspected to avoid restating their weaker obstructions as this run’s result.
The closest prior construction behind the retained global theorem is Garoufalidis–Yu, The 3d-index of the 3d-skein module via the quantum trace map, author PDF dated 6 August 2025, Sections 5.1–5.2 and Theorem 5.3. This run uses its convergence methodology only through the prior full-root proof; it does not newly claim that GY’s stated even/homological restrictions have disappeared by citation. Its retained source ledger records the author-PDF hash fe39f211f0d223bc452833f657730576802a0f5a3b0543844618c76c1e6c121d.
Work proved in this packet
The shifted native degree/phase substitution, coefficient stopping boundary, character-twisted left-seed functional and exact shear cancellation are elementary consequences proved here from the retained and sourced ingredients. The three-tetrahedron witness, its finite correct-sided identity, its strict-angle leading-degree analysis, and its necessary actual-incidence exclusion are proved explicitly and verified independently by exact code.
No comprehensive novelty or first-priority determination was performed. The result is a supporting obstruction to a particular inference, not a recognized conjecture resolution or a claim of a substantial new topological theorem.