Local collar continuation: source ledger
8 September 2026. Primary mathematical sources and the existing Lab proof record only. Source hashes identify inspected bytes, not publisher-certified checksums.
Contents
Retrieval and continuity
The live stable handoff and program were fetched read-only. Their first public search opens failed, but direct public retrieval subsequently succeeded. The handoff selects the signed additive six-root peripheral lift and raw named-action dictionary after the CK comparison publication. Its older author-contact sentence has been superseded by the task owner’s report that Chen and Kricker were emailed with Joshua Gay copied; no reply or endorsement is assumed.
The existing publication, active bridge proof/audit, earlier generic-boundary note, positive-geometric note, and classical empty-sector note were read from the owner’s authorized read-only snapshot paths. The publication and relevant bridge material were inspected in detail; the older results’ statements and dependency boundaries were checked, not independently re-proved in full. No Site content was edited or deployed in this research continuation.
The local prior six-root proof, audit, source ledger and entire exact verifier were read as claims to test. The verifier was re-run and its quotient-stage argument compared to the primary GY construction and the whole GY-index Appendix A.
New decisive primary reading
| Source | Exact places | Evidence supplied and limit |
|---|---|---|
| Panitch–Park, published PP1 | Definition 3.3; Remarks 3.4–3.5, printed pp. 2264–2265; Remark 3.9 and Proposition 3.10, pp. 2266–2267 | Actual unweighted marking reversal/state flip, complete ordinary-to-symmetric cup and cap conversion, and the distinct weighted self-duality. Pages were rendered and visually read. These geometric operations belong to PP, not this note. |
| Same PP1 | Theorem 3.21 and its rescaled action relations; Remark 4.10 | Explains why the weighted self-duality is suited to a balanced action construction and cannot simply replace unweighted state flip in a same-state tensor contraction. The failed replacement is not a claimed defect in PP’s theorem. |
| Garoufalidis–Yu, published GY | Sections 2.1–2.2; Figure 13 and (62)–(64); (24)–(32) | Ambient orientation, dual-surface collar, actual bare-edge standard arcs, native minus-state root convention and corner coefficients. The Figure 13 page was rendered. |
| Same GY | Sections 4.6–4.10; Lemmas 4.17, 4.21–4.22; Theorem 4.18, Corollary 4.19; (60); Theorem 4.25; Remark 5.1 | Prequotient standard-arc spanning, off-diagonal annihilation, native counit and full six-root target. No inverse to opposite-root identification is inferred. |
| Garoufalidis–Yu, GY-index author revision dated 6 August 2025 | (7)–(22), (29)–(31), (92)–(95); full Appendix A, pp. 30–36 | Parameter map, matching-state splitting, annular spanning/counit, native peripheral theorem and all prequotient geometric lemmas reused in the extension. The admissible diagram construction remains an imported input. |
| Chen–Kricker, 2606.13268v1 | Section 1, Figure 1.1; Definition 2.2; Section 4.1, Figure 4.2, Definition 4.1 and Remark 4.2 | Actual opposite collar, marking direction, cyclic shape labels and corner-ideal sides. Figures on pp. 3, 45 and 46 were visually inspected. |
| Same CK | Sections 4.2–4.3, especially Figure 4.4, Lemma 4.6, Theorems 4.8–4.9; Theorem 5.34 | Plus-state shape convention, full off-diagonal quotient, local standard-arc spanning and already-proved adjusted named comparison. The raw dictionary is supplied by the written local square, not read into the theorem without work. |
| Panitch–Park, PP2 2509.09100v1 | Definition 2.2 and footnote 5, Theorem 2.20, Remark 2.21 | Confirms symmetric ribbon convention, explicitly points to PP1 Remark 3.5, and supplies the normalized branch data used in the prior transport. |
| CK degree-zero-descent publication | Theorem 1.1, Sections 6–7, hostile audit | Existing mixed-sided comparison isomorphism and Eulerian original-PP branch transport. The current continuation does not re-prove the entire intersection theorem or its independent verifier. |
| Positive-geometric filling note | Result/hypotheses, Sections 1–4 | Conditional nonvanishing transferred through a boundary-linear quotient. No extension beyond its stated chamber is claimed. |
Exact inspected source snapshots
The retained source copies were freshly re-read and their hashes recomputed; they were not all newly downloaded in this continuation. This distinguishes an independent reread from a claimed new download. The current CK HTML was also reopened successfully. Source PDFs and page images are not redistributed.
0b7c6ffe350d0c625d27fdd6ee4795969e8f649918fe6611e170e52483d8af59 GY published PDF
fe39f211f0d223bc452833f657730576802a0f5a3b0543844618c76c1e6c121d GY-index author revision
3a4758a2776811bea150aae0cc64fe78994e47edc06e916f59b80a9ab3716ed8 CK 2606.13268v1 PDF
df01b8de62d4495af2f3ff7d0bba2ec0858e709951686cf4b99adf107e93d280 PP1 published PDF
7323a21fc3aa4206b20fbd283b42ac829499a916fd75cab3766d779908fe57e2 PP2 2509.09100v1 PDF
ecbeb73e147aeb2a347f87d0d76e0d8dc5011b95652d6232cea3929db336b082 PR 2609.02706v1 PDFSearch boundary and credit
A bounded fresh query looked for stated-skein marking reversal/state flip, splitting/counit compatibility, and GY/CK lantern conventions. It returned primary Costantino–Lê literature and the GY-index source as leads; no uninspected lead is used in the proof. The decisive facts were found in the retained published PP1 itself. No first-priority or exhaustive novelty claim follows from this search.
The known operations, trace constructions and primary comparison theorems are credited to their authors throughout the proof. The local tensor verifier is new audit code, not a proof assistant or a replacement for those source theorems. It performs only exact Laurent arithmetic, matrix identities and a formal reciprocal-gauge check. It samples no manifolds, slopes, triangulations or skein configurations.
Preserved limitations
The mixed-sided Laurent reading of CK is part of the mathematical statement; no author erratum has been confirmed. The all-slope peripheral extension is generic. No target-action canonicity across triangulations, survival of all global sign sectors, unrestricted filling nonvanishing, solution of PR 7.1, external review or author endorsement is claimed.