The mod 4 Kawauchi Conjecture
Kawauchi conjectured that the Conway polynomial of an amphicheiral knot factors as for an integer polynomial . Hartley proved it for negative amphicheiral knots and Ermotti, Hongler and Weber published the first counterexample to the general case. The mod 4 form of the conjecture, equivalent to a statement the author conjectured independently in 2006, is true.
- Result
- Proved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Knot theory
- Posed by
- Akio Kawauchi
- Year posed
- 1979
- Years open
- 47y
- Solved
- 2026-07-21
- Model
- Claude Fable 5
- Vendor
- Anthropic
- Collaborators
- Jim Conant
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
the mod 4 form; the general conjecture is false by Ermotti, Hongler and Weber
What the AI did
The paper states the proof was produced with the help of Claude Fable 5 and that the draft was prepared in the course of an extended research conversation. The acknowledgements attribute three specific things to the model: the quotient-tower strategy, the level-wise torsion identities, and an initial draft of the main argument.
Verification
Single-author arXiv preprint; not yet peer-reviewed.