FPRD LabShare an approach

Sources and priority boundaries

Primary sources checked on 8 September 2026. No author contact or external validation is implied. Source metadata and exact byte hashes are recorded in source-snapshots.json; full primary texts are not redistributed.

Contents

Formal dependencies and intellectual influences

Source Inspected mathematical content Role
Garoufalidis–Hodgson–Hoffman–Rubinstein, The 3D-index and normal surfaces, arXiv:1604.02688v1 Sections 6–8; Corollary 8.12; Lemma 10.8; Appendix A Actual incidence/normal-class dictionary, boundary and Euler maps, and complete-angle positivity. The normal-surface interpretation directly influenced the approach.
Futer–Guéritaud, From angled triangulations to hyperbolic structures, arXiv:1004.0440v2 Lemmas 4.4–4.5 and Section 6 Leading–trailing deformations and angular filling slices. The proof gives its own normalized matrix calculation; the method is established prior work.
Garoufalidis–Yu, The 3d-index of the 3d-skein module via the quantum trace map, author PDF dated 6 August 2025 Sections 5.1–5.3, 5.5 and Appendix A Seed averaging, normal-surface convergence method, and native peripheral action, used through the retained full-root proof packets. The current author PDF has the same hash as the earlier inspected copy.
Garoufalidis, The 3D index of an ideal triangulation and angle structures, arXiv:1208.1663v2 Section 3 and Section 4.5 Tetrahedron-index identities underlying the retained detector. The index itself originates with Dimofte–Gaiotto–Gukov.

The source-normalized formal Euler map takes values −2,0,−1-2,0,-1 on an edge row, peripheral row, and tetrahedron vector. The proof’s displayed scalar cancellation is an independent calculation with those actual rows; it does not claim these Euler facts, normal-surface positivity, or the index degree formula as new.

Closest comparison and external problem

Celoria–Hodgson–Rubinstein, The 3D index and Dehn filling, arXiv:2509.09886v2, Theorem 6.2, gives an important existing surgery result under standard-cusp and efficiency hypotheses. Section 11 studies large fillings; Section 15 retains broader questions. This note does not identify its native functional with that invariant, remove the source’s hypotheses, or claim a new large-surgery phenomenon solely from the bound proved here.

Panitch–Romo, On the length conjecture for twist knots, arXiv:2609.02706v1, Conjecture 7.1, asks for the compatible nontrivial Dehn-filled quotient in general. The current abstract page lists the 2 September 2026 first version. The two-angle result does not settle arbitrary triangulations or fillings, and does not close that conjecture.

Version checks

The current abstract pages list GHHR v1 (10 April 2016), Futer–Guéritaud v2 (9 November 2010), Garoufalidis v2 (7 October 2015), Celoria–Hodgson–Rubinstein v2 (19 December 2025), and Panitch–Romo v1 (2 September 2026). Garoufalidis–Yu’s arXiv page still lists v1 (7 June 2024); the separately pinned author PDF is dated 6 August 2025. Crawler dates are not treated as mathematical revision dates.

Retained project dependencies

The live canonical handoff and live longitude-difference proof were retrieved directly; both exactly matched the inspected corresponding input files. The preceding longitude audit and exact code were read. The retained inputs are:

No new peripheral-sign, comparison, or source-erratum claim is made. The older strict positive geometric theorem retains its own scope.

Limited contribution claimed

The actual raw-row map λ↦Xλ\lambda\mapsto X_\lambda, exact cancellation of the filling correction against the longitude Weyl term, all-plus dependency argument, and two-angle application are proved in this packet. The explicit slope estimate is a direct quantitative use of existing angular deformation ideas.

No comprehensive novelty or first-priority determination was performed. The result is not ranked by recency or by an activity count. It remains a conditional research note, not a Publication or a recognized open-conjecture resolution.