Source ledger — generic boundary reconstruction and nonvanishing
Checked 8 September 2026. Version identifiers below are those of the actual primary texts inspected. Files were read in full at the relevant sections; local PDF text extraction was supplemented with visual inspection of the GJV two-point diagram. Downloaded primary full texts are not included in the public archive. Hashes identify the inspected working copies.
| Source | Exact version and location | Role and limit |
|---|---|---|
| GJV | 2409.05613v1, Theorems 1.5 and 6.1; Proposition 6.3; Section 7.1 | Formal input: generic torus category generation; explicit two-strand reduction. Category theorem belongs to Gunningham, Jordan and Vazirani. |
| GJS | 1908.05233v4, Theorems 2.5 and 4.1; Proposition 4.3 | Formal input: categorical excision. The older two-handlebody sufficient condition alone does not give arbitrary-piece algebra excision. |
| GY index | 2406.04918v1, Section 3.3, (29)–(31); Remark 3.1; Section 5.5 and Theorem 5.7; Appendix A | Formal input: identified target, all-edge ideal generated by N−r independent edges, full peripheral action and trace intertwining. Appendix A is not asserted here to prove an extended six-root theorem. |
| GY trace | 2403.12424v1, Section 5.1 and Remark 5.1 | Trace construction and possibility of retaining an extra opposite-root generator. |
| PP original | 2403.12850v1, Section 5.2; Theorems 5.5–5.6 | Original face-suspension image target and ambient sided relation structure. |
| CK | 2606.13268v1, Theorems 1.3 and 4.9; discussion before 4.9; (5.6) and (5.7); Definition 5.22; Remark 5.26; Conjecture 5.27 | Formal input: extended GY comparison and PP surjection. The normalizer lemma proves a sufficient kernel-invariance condition without assuming comparison injectivity. |
| PP UV–IR | 2509.09100v1, Remark 2.21; Definition 2.22 and footnote 11; Theorem 2.25 | Modified opposite-root target and two scaling branches. Matching target presentations alone does not match the named trace. |
| FG | 9806107v1, Theorems 2 and 3; Section 5 | Formal input: invariant quantum-torus presentation and two solid-torus vacuum-ideal generators, including the negative framing coefficient. The note takes the opposite collar explicitly. |
| PR | 2609.02706v1, Section 7, Conjecture 7.1 | Open objective; not a theorem dependency. The note does not assert all conjectural fillings satisfy the local regularity hypothesis. |
Inspection hashes
SHA-256 of each downloaded source file (not an assertion of a canonical publisher checksum):
2409.05613.pdf:4b03775361ed38b47b0e577a58d63464cb37706e84510678dfaf171d3f124f051908.05233v4.html:1656119ce118e4330b6fc2d3fcb904b5110ec7f13755f08b34344de6f9f0eb572406.04918.pdf:634e4d8ad74b391c4d4a8a4558c015d887db1ee3b69c43d22dc7a69c4e480e8a2403.12424.pdf:b3fbe3ce3703250c569c6198f00e2d6607cb184eabf38cf5b884b8da7566d3c92403.12850.html:7a47eb7ef407b877033f967884e5ff136c65f7f7ded8bb4e32b6c7339eed4b6a2606.13268v1.html:1f017ab31fce6347740a1ed7c0b2dd0b36986345fc4bbabafa4240225be2576c2509.09100v1.html:39777b6fb307cba58a0b254e6f56bb40630716cdff1247ef003c9591a49b6529math9806107.pdf:ad4acfbcf2e5058d22e10a32762c1fd588b6191cd4c6bfd13a0d4566c3d7374f2609.02706v1.html:93a3bc88b369854d8dfb8c61e6ae0e363c6299db46c2cfe3eed6c08658af5fc0
Proof audit and credit
- Generic compact generation and the two-point identity are GJV results. Categorical gluing is the GJS/Walker excision input. The finite-frame endpoint formula and ordinary generic torus-algebra gluing in this note are explicit consequences of those inputs.
- The cokernel theorem uses FG’s ideal generators, but its two displayed mutually inverse maps and their noncommutative factorizations are proved directly in the note. No novelty priority is claimed.
- The regular-intersection theorem uses GY’s exact presentation and commuting operators. The regular-sequence syzygy statement is proved by induction in the note. Torsion-freeness follows by lifting those syzygies; the source-to-formal quotient map is exhibited. It is not inferred from a nonzero classical fiber or a truncated calculation.
- PP/CK influence the ambient normalizer approach. Its proof is explicit, but it is a sufficient condition for transferring verified multiplication operators, not a proof of the missing globally normalized PP action.
- No claim that all intended geometric fillings satisfy the local regular sequence is made. No canonical PP trace identification follows solely from a matching quantum-torus presentation. No Publication or external novelty assessment is claimed.