Source and limited priority ledger

Checked 8 September 2026. Only primary sources are used as mathematical evidence. Downloaded papers and their images are working copies, not redistributed in this packet. Hashes identify those inspected copies, not canonical publisher checksums.

Contents

Formal mathematical inputs

Source	Exact location used	Role and limit
Qingjing Chen and Andrew Kricker, On 3d Quantum Trace Maps, arXiv:2606.13268v1, 11 June 2026	Definitions 3.1 and 3.7; Definition 5.7; Definitions 5.17 and 5.22; Lemma 5.18 (p. 73); equation (5.6) (p. 75); Proposition 5.25 (pp. 77–80); Remark 5.26 and Conjecture 5.27 (p. 80); Theorem 5.34 (pp. 86–87)	Exact ambient image target, complete sided relations, generator-matching surjection, and already proved named-trace intertwining. The new proof addresses their explicitly stated injectivity conjecture. No source injectivity is assumed.
Same CK source	Introduction Section 1.2; Section 4.1, especially Remark 4.2; Lemma 4.6; Section 4.3 and Theorem 4.9	Their extended GY comparison is convention-adjusted; the source explicitly distinguishes opposite-root identification and different labeling/orientation conventions. It is not GY-index Theorem 5.7 in unchanged coordinates.
Samuel Panitch and Sunghyuk Park, 3d quantum trace map, Algebraic & Geometric Topology 26 (2026), 2255–2314, DOI 10.2140/agt.2026.26.2255	Section 5.2, especially its displayed definition of the ambient quotient; Proposition 5.8; Remark 5.9; Lemma 5.11; Definition 5.13; face trace in Theorem 5.5	Independently checks the actual PP ambient relation module (V_+U+UV_-), including the side on which each relation is multiplied. Original constants and edge/vertex signs. We do not assume the image target equals the desired shape quotient.
Panitch–Park, arXiv:2403.12850v1	Same Section 5.2 locations, readable mathematical HTML	Cross-check against original preprint. The published primary PDF was freshly downloaded and inspected as well.
Panitch–Park, Compatibility of quantum trace and UV-IR maps, arXiv:2509.09100v1, 11 September 2025	Theorem 2.20, Remark 2.21 and footnote 10; Definition 2.22 and footnote 11	Exact triangle/bigon coefficients and scaling branches; explicitly identified opposite-root target. CK Lemma 5.18 uses this normalization. The local scaling is sourced; the global Eulerian extension comes from the preceding Lab note.
Stavros Garoufalidis and Tao Yu, A quantum trace map for 3-manifolds, Advances in Mathematics 486 (2026), 110735, DOI 10.1016/j.aim.2025.110735	Section 4.10, equations (62)–(70), Theorem 4.25; Section 5.1, Remark 5.1	Confirms the six-root skew matrix, standard diagonal arcs, and the genuine extended-versus-identified distinction. This is the published version cited by CK.
Garoufalidis–Yu, The 3d-index of the 3d-skein module via the quantum trace map, arXiv:2406.04918v1	Section 3.3, (29)–(31); Remark 3.1; (89)–(92), Theorem 5.7; Appendix A	The active handoff’s identified target and boundary theorem. Inspected to determine exactly what cannot be imported into the six-root target without proof.
Garoufalidis–Yu, author-hosted revision dated 6 August 2025	Same Section 3.3 and Theorem 5.7; Appendix A; added Section 5.6, especially (97)	Fresh revision cross-check: opposite roots are still identified for Theorem 5.7. Its chirality formula explicitly changes states, inverts variables, swaps labels, and conjugates coefficients, reinforcing the need for a real convention dictionary. No unpublished six-root peripheral theorem is inferred.
Samuel Panitch and Mauricio Romo, arXiv:2609.02706v1	Section 7, Conjecture 7.1, from current handoff and live primary record	Larger Dehn-filling objective, not a theorem input. Remains open here.

Inspected source SHA-256 values

Freshly downloaded during this attack:

3a4758a2776811bea150aae0cc64fe78994e47edc06e916f59b80a9ab3716ed8  ck-2606.13268v1.pdf
df01b8de62d4495af2f3ff7d0bba2ec0858e709951686cf4b99adf107e93d280  pp-published-2026.pdf
7323a21fc3aa4206b20fbd283b42ac829499a916fd75cab3766d779908fe57e2  pp2-2509.09100v1.pdf
0b7c6ffe350d0c625d27fdd6ee4795969e8f649918fe6611e170e52483d8af59  gy-published-2026.pdf
fe39f211f0d223bc452833f657730576802a0f5a3b0543844618c76c1e6c121d  gy-index-author-2025.pdf

Earlier retained primary snapshots inspected again:

634e4d8ad74b391c4d4a8a4558c015d887db1ee3b69c43d22dc7a69c4e480e8a  2406.04918.pdf
1f017ab31fce6347740a1ed7c0b2dd0b36986345fc4bbabafa4240225be2576c  2606.13268v1.html
39777b6fb307cba58a0b254e6f56bb40630716cdff1247ef003c9591a49b6529  2509.09100v1.html
7a47eb7ef407b877033f967884e5ff136c65f7f7ded8bb4e32b6c7339eed4b6a  2403.12850.html

The first whole-PDF CK text extraction stopped partway through p. 74; pages 75–87 were explicitly extracted separately, and pp. 80–81 were visually rendered and inspected. The exact statement of Conjecture 5.27 was therefore checked directly in the primary PDF, not inferred from an abstract or secondary summary. GY-index pp. 30–31, including the standard/substandard-arc geometry, were also visually inspected. These were read-only PDF-skill operations.

Sidedness inconsistency in CK

Definition 5.7(i) defines a right ideal and then once calls its global extension a left ideal. We resolve the intended target using their equation (5.6), Definition 5.11(i), the right-multiplication calculation in Proposition 5.25, and PP1’s explicit (V_+U+UV_-) presentation. They all use a right-generated tetrahedron relation module. The candidate proof does not assert an isomorphism for a different target obtained by imposing the two-sided closure of the tetrahedron Lagrangians.

Fresh limited priority check

The exact arXiv submission histories for CK and PP2 were checked live. Both primary records exposed only v1. CK’s currently served v1 still states Conjecture 5.27 as conjectural, and the published PP1 text still defines its target as an ambient image.

Targeted searches included:

"On 3d Quantum Trace Maps" "injectivity"
"Panitch" "Park" "quantum gluing module" "injective"
"Chen" "Kricker" "quantum trace"
site.arxiv.org "quantum gluing" "grading" Panitch
site.arxiv.org "Chen" "Kricker" "injective"

The primary author research lists of Samuel Panitch and Sunghyuk Park were checked for current related papers. Searches also located Brown–Jordan’s Parabolic skein modules, arXiv:2505.14836, as adjacent literature; its appearance is not evidence of a proof of this particular comparison conjecture. No primary-source resolution of CK Conjecture 5.27 was located in this bounded check.

This is not an exhaustive priority audit. No claim of first discovery is made. Secondary indexing sites and AI summaries were not used to support any mathematical step. The explicit primary conjecture, not the absence of search hits, is the recognized-problem calibration.

Ownership of the contribution

The trace constructions belong to GY and PP. The comparison construction, its surjectivity, and the named-trace theorem belong to CK. Much of the local multiplication used here appears in CK Proposition 5.25. The Lab contribution is the exact equal-ideal reformulation and the zero-degree retraction argument supplying the reverse ambient intersection inclusion. The extension of GY-index peripheral Theorem 5.7 to all six-root sectors is neither attributed to the sources nor claimed by the Lab.