Problem detail · source-aware
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Kawauchi conjectured that the Conway polynomial of an amphicheiral knot factors as $\nabla_K(z) = f(z)f(-z)$ for an integer polynomial $f$. 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.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
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.
Provider: Anthropic · Prompt public: unknown · Independence: unknown
Single-author arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
the mod 4 form; the general conjecture is false by Ermotti, Hongler and Weber
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.