Sources, dependencies, and influence
All fresh checks below were made on 8 September 2026.
| Source | Exact use | Status |
|---|---|---|
| Panitch–Park, published AGT 26 (2026), 2255–2314 | Definition 5.16 and Theorem 5.21 for the even shape module and its forward map; Sections 6.2.1–6.2.3 for full six-root traces; p. 2310 for the framing correction; Figures 12–13 for the links; published Question 7.3 for injectivity scope. | Publisher PDF downloaded successfully and text read. Printed pp. 2307, 2308 and 2310 visually inspected. Formal dependency. |
| Panitch–Park, arXiv:2403.12850v1 | Located explicit computations before consulting journal version. Initial cable expansion agrees; final old simplification and old universal injectivity conjecture are not used. | Preprint and current arXiv metadata read; journal version governs. |
| GY-index, arXiv:2406.04918v1 | Section 3.3 identified edge redundancy; Figure 11, equations (98)–(100) for discovery and independent formula/framing comparison. | PDF read; figure/formula page visually inspected. |
| GY quantum trace, arXiv:2403.12424v1 | Equation (108) for the actual meridian z0/w1 in the figure-eight presentation. | PDF read. |
| Bullock–LoFaro, AGT 5 (2005), 107–118 | Theorem 2.1 and Figure 1: spanning family mu^n b^(j), j=0,1,2. Required to annihilate the whole trace image, not just the displayed generators. | Original PDF read and diagram inspected. |
| Garoufalidis, tetrahedron index | Definition 3.1 and Section 4.5 for the index recurrence and normalization. | Fresh primary-source read; formal dependency. |
| Garoufalidis–Hodgson–Hoffman–Rubinstein | Exact J-index degree formula, giving quadratic all-input convergence and the nonzero unit. | Fresh primary-source read; formal dependency. |
| Native collar and peripheral-action note | Named meridian action on all inputs, full branch dictionary, and correct side reversal. | Retained internal theorem; not independently re-proved by this finite verifier. |
| Previous central-meridian note | Minimal-quotient question and linear exact sequence. | Prior Lab work. Its balanced vacuum certificate alone did not supply the new witness. |
| Panitch–Romo, arXiv:2609.02706v1, Section 7 | Distinction between a nonzero quotient and a nonzero descended trace. | Fresh source checked; no unrestricted resolution claimed. |
Intellectual influence separate from proof dependencies
The twist-knot basis suggested searching for a degree-two relation over the meridian action. The classical distinction between reducible and irreducible character components suggested why such a kernel might exist, but no classical specialization or A-polynomial is used to infer the quantum identity. The tetrahedron-index seed originates with Dimofte–Gaiotto–Gukov; its rigorous recurrence and convergence framework are credited through Garoufalidis and GHHR. The new parity insertion reuses that framework.
The fixed-datum relation, correct-sided certificate, and image-annihilating parity insertion are the conclusions of this attack. Their novelty has not been established. No source author has reviewed or endorsed them.