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The mod 4 Kawauchi Conjecture

Geometry & topology · posed by Akio Kawauchi, 1979 · solved

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Statement

Kawauchi conjectured that the Conway polynomial of an amphicheiral knot factors as ∇K(z)=f(z)f(−z)\nabla_K(z) = f(z)f(-z) for an integer polynomial ff. 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.

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  1. proof attempt · #1

    Jim Conant, using Claude Fable 5

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

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    ai co developed
    — a person and a model developed the result together.

    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.

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