Benefit Ledger · provisional · Mathematics
On 21 July 2026 Jim Conant posted a proof that the Conway polynomial of an amphicheiral knot satisfies ∇_K ≡ f(z)f(−z) (mod 4), a strengthening he had conjectured after the integral Kawauchi conjecture failed. He credits Claude Fable 5 with help producing the proof.
Current score
+0.20
A proof of a named knot-theory conjecture is notable (tier 2). Fable 5 co-developed the argument (0.55). Evidence is an arXiv preprint (0.35). Realization is a public proof the author verified (0.50).
Kawauchi’s original conjecture on Conway polynomials of amphicheiral knots is false in general; Ermotti–Hongler–Weber published a counterexample. Conant’s mod-4 version remained. arXiv:2607.18655 proves it as a consequence of a stronger integral statement. The abstract says the mathematical content was produced with the help of Claude Fable 5. This is a named Fable 5 release, not version-unspecified Claude.
Named Claude release credited with help producing the mod-4 Kawauchi proof.
The paper states the mathematical content was produced with the help of Claude Fable 5.
Attribution 0.5500 · Credit share 100% · Anthropic
Conant proved that amphicheiral knots satisfy the mod-4 Kawauchi congruence for the Conway polynomial, with help from Claude Fable 5.
outcome · supported
primary sources
arXiv · preprint · 21 Jul 2026
13 Sep 2026 · 0.00 → 0.20
Imported events under methodology 0.1.
