What was already known
Integer factorization was known for certain positive and negative amphicheiral knots, while a counterexample defeated the unrestricted integer conjecture. Conant’s 2006 mod-4 weakening remained open in general.
AI involvement
Conant credits Claude Fable 5 with the quotient-tower strategy and level-wise torsion identities. He originated the conjecture, heavily revised the draft, independently verified the central Claude-produced results and wrote the final exposition.
Claude supplied the retained quotient-tower strategy and torsion identities; Conant directed, revised and verified the mathematical work.
Importance
The result closes the mod-4 conjecture for all amphicheiral knots.
Limitations
Conant’s reported independent check excludes Appendix B example calculations; those examples are outside the assessed theorem.
Technical verification
Conant explicitly reports independent verification of Claude-produced results apart from Appendix B examples. This is a completed author check of the mod-4 theorem and its AI-origin proof ingredients, with the example exception kept outside the assessed claim.
Independent checking
Independent mathematical verification during extensive revision
- Checker
- Jim Conant, human author
- Scope
- Claude-produced quotient-tower and torsion results supporting the mod-4 theorem, excluding Appendix B example calculations
- Basis
- Reported by the linked checker
Human understanding
Conant's extensive revision and detailed explanation of the tower, palindromic normal form and integral identity document a human account of the central mechanism.
Correction and publication history
Initial publication of this result.
Read this published revision