Six-root peripheral lift: primary-source ledger
Checked 8 September 2026. Primary sources were read afresh at the relevant locations. The current source records and the independently retrieved author-hosted revision were compared with earlier working copies. Primary PDFs are not redistributed in this evidence archive.
Contents
Mathematical dependencies and exact scope
| Source | Inspected locations | What it supplies; what it does not |
|---|---|---|
| Garoufalidis-Yu, A quantum trace map for 3-manifolds, published PDF, Advances in Mathematics 486 (2026), 110735; arXiv:2403.12424 | Sections 4.6, 4.9-4.10; (62)-(70); Lemmas 4.21-4.22; Theorem 4.25; Remark 5.1 | Full six-root local target, vanishing of standard off-diagonal terms before opposite-root identification, standard-arc spanning, and existence of the extended named trace. The published paper’s later theorems are not silently extended to arbitrary unrelated constructions. |
| Garoufalidis-Yu, The 3d-index of the 3d-skein module via the quantum trace map, author-hosted revision dated 6 August 2025; arXiv record | Sections 2.2-2.3; (7)-(17); Section 3.3, (29)-(31), Remark 3.1; Section 5.2, (53)-(56); Section 5.5, (92)-(95); Section 5.6, (97); full Appendix A, pp. 30-36 | Exact parameter, native left-tetrahedron/right-edge sidedness, diagonal standard-arc states, NZ pairing, torus product convention, actual peripheral theorem, its prequotient diagrammatic lemmas and two-state proof. The new proof uses those prequotient lemmas, not an inverse to the identified target. |
| Chen-Kricker, On 3d Quantum Trace Maps, arXiv:2606.13268v1 | Definition 2.2, pp. 12-13; Definition 2.15; Section 4.1 and Remark 4.2, pp. 44-46; Section 4.2, pp. 48-50; Theorems 4.9 and 5.34 | Opposite lantern collar/product, CK’s plus-state shape convention, corner constants, and existing convention-adjusted named comparisons. The source warns that its GY convention is adjusted. It does not establish the particular raw collar/state dictionary asserted as still missing in this note. |
| Panitch-Park, 3d quantum trace map, published PDF, Algebraic & Geometric Topology 26 (2026), 2255-2314; arXiv:2403.12850v1 | Stated ribbon relations; face-suspension map and original constants; Section 5.2 | Original PP named construction and symmetric ribbon/framing convention. The previous Lab normalization theorem, not new work here, transports the original branch to CK’s normalized branch. |
| Panitch-Park, Compatibility of quantum trace and UV-IR maps, arXiv:2509.09100v1 | Section 2.1, Definition 2.2 and footnote 5; Theorem 2.20, Remark 2.21; Definition 2.22 and footnote 11 | Exact symmetric cup and half-twist constants, two normalization branches, and the explicit extra opposite-root quotient. Its label/prime convention must not be inferred from the shared letters alone. |
| Frohman-Gelca, Skein modules and the noncommutative torus, Transactions of the AMS 352 (2000), 4877-4888 | Product-to-sum theorem in the form recalled in GYI (94) | Torus skein embedding and product-to-sum. Used through the primary GYI restatement; no claim of independently re-proving the original paper. |
| Bullock-Przytycki, Multiplicative structure of Kauffman bracket skein module quantizations, Proceedings of the AMS 128 (2000), 923-931 | Three-generator statement explicitly invoked in GYI Appendix A | Three-generation. The reduction to two generators over the generic field is the elementary commutator calculation in this packet. |
| Panitch-Romo, On the length conjecture for twist knots, arXiv:2609.02706v1 | Section 7, Conjecture 7.1 | Larger objective: a nontrivial compatible Dehn-filled quotient. Neither native peripheral linearity nor a target-presentation isomorphism establishes that full conjecture. |
Fresh source-snapshot checksums
These identify the freshly retrieved files, not publisher-certified checksums.
3a4758a2776811bea150aae0cc64fe78994e47edc06e916f59b80a9ab3716ed8 CK arXiv:2606.13268v1 PDF
0b7c6ffe350d0c625d27fdd6ee4795969e8f649918fe6611e170e52483d8af59 GY published PDF
fe39f211f0d223bc452833f657730576802a0f5a3b0543844618c76c1e6c121d GY-index author revision PDF
df01b8de62d4495af2f3ff7d0bba2ec0858e709951686cf4b99adf107e93d280 PP1 published PDF
7323a21fc3aa4206b20fbd283b42ac829499a916fd75cab3766d779908fe57e2 PP2 arXiv:2509.09100v1 PDF
ecbeb73e147aeb2a347f87d0d76e0d8dc5011b95652d6232cea3929db336b082 PR arXiv:2609.02706v1 PDFThe fresh GY-index author revision, GY published PDF, CK v1, PP1 and PP2 copies matched the relevant earlier retained snapshot hashes. The live arXiv records for the two GY papers still exposed v1; the newer author-hosted GY-index revision was therefore used for its Appendix A and added chirality section. The GY HTML endpoints returned no usable paper, so the fresh primary PDFs were used instead. This is a source-format issue, not a mathematical blocker.
Read-only PDF rendering was used to inspect native collar orientation, the tetrahedral label drawing, the stated boundary relations, and the CK collar/marking drawings. Rendering checks are not evidence for the unproved geometric dictionary.
Bounded novelty check
Targeted searches on 8 September 2026 included site.arxiv.org "quantum trace" "peripheral" "six", site.arxiv.org "quantum trace" "opposite" "peripheral", and a search for the GY-index title and Theorem 5.7. No primary-source statement of this precise generic six-root extension was located in that bounded pass.
This does not certify novelty. The native extension reuses the source proof very closely and may be known to its authors or implicit in related work. The two-generator commutator is elementary; it is not presented as a newly discovered general fact. The likely significance is useful internal progress on a comparison obligation, not a publication-level boundary move. Novelty: unknown.
Searches for stated-skein boundary reversal/antipode literature were also made as leads for the remaining dictionary. No uninspected search result is used as a mathematical input in the theorem.
Intellectual credit
GY supply the trace, full local target, and virtually all geometric input. Their Appendix A directly influenced the extension. Frohman-Gelca and Bullock-Przytycki supply the torus algebra facts. Neumann-Zagier supply the symplectic identities in the form used by GYI. CK supply the convention-adjusted named comparison and explicit alternate target. PP supply their independent trace and ribbon conventions.
The Lab’s contribution in this run is the quotient-stage audit that retains actual bare-edge exponents, the additive extension via two named insertions, and the explicit accounting of what that proves and what is still missing in the raw named bridge.