{"data":{"event":{"id":"b57f8c16-907c-4ee7-b8c4-4891927d3921","slug":"claude-fable-5-mod4-kawauchi","title":"Conant, with Claude Fable 5, proves the mod-4 Kawauchi conjecture","short_summary":"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.","full_description":"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.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-07-21T00:00:00.000Z","discovery_date":"2026-07-21T00:00:00.000Z","first_published_date":"2026-07-21T00:00:00.000Z","last_reviewed_date":"2026-07-21T00:00:00.000Z","geographic_scope":"International","affected_population":"Geometric topology research community","base_impact_tier":2,"base_score":"3.00","attribution_multiplier":"0.5500","evidence_multiplier":"0.3500","realization_multiplier":"0.5000","durability_multiplier":"0.7000","current_event_score":"0.202100","confidence_level":"medium","score_explanation":"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).","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-07-21T00:00:00.000Z","created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-13T22:56:05.431Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.1"},"contributions":[{"id":"f082c1fd-3d86-4355-b3ea-c4dc77ec5e6d","event_id":"b57f8c16-907c-4ee7-b8c4-4891927d3921","model_id":"19e2b5dd-4f37-446a-8344-48196c5acf5a","role_description":"Named Claude release credited with help producing the mod-4 Kawauchi proof.","attribution_multiplier":"0.5500","credit_share":"1.0000","contribution_score":"0.202100","attribution_rationale":"The paper states the mathematical content was produced with the help of Claude Fable 5.","attribution_confidence":"medium","first_used_date":"2026-07-21T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T22:56:05.431Z","model_slug":"claude-fable-5","model_name":"Claude Fable 5","identity_class":"named_release","is_internal":false,"family_name":"Claude","family_slug":"anthropic-claude","organization_name":"Anthropic","organization_slug":"anthropic"}],"sources":[{"id":"5d908391-64d6-4fb6-8972-9ea2db9a9ec0","event_id":"b57f8c16-907c-4ee7-b8c4-4891927d3921","url":"https://arxiv.org/abs/2607.18655","canonical_url":"https://arxiv.org/abs/2607.18655","source_type":"preprint","publisher":"arXiv","author":null,"publication_date":"2026-07-21T00:00:00.000Z","retrieved_at":"2026-09-13T22:56:05.431Z","title":"A proof of the mod 4 Kawauchi Conjecture","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":true,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T22:56:05.431Z"}],"claims":[{"id":"30f15cf4-a4bb-4099-8f4e-3b1805bac88a","event_id":"b57f8c16-907c-4ee7-b8c4-4891927d3921","claim_text":"Conant proved that amphicheiral knots satisfy the mod-4 Kawauchi congruence for the Conway polynomial, with help from Claude Fable 5.","claim_type":"outcome","claim_status":"supported","confidence_score":null,"created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-13T22:56:05.431Z"}],"revisions":[{"id":"10120c5c-f432-4455-9b55-7c9148fa944c","event_id":"b57f8c16-907c-4ee7-b8c4-4891927d3921","model_id":null,"previous_score":"0.000000","new_score":"0.202100","previous_factors":{},"new_factors":{"evidence":0.35,"base_score":3,"durability":0.7,"attribution":0.55,"realization":0.5},"change_reason":"Imported events under methodology 0.1.","trigger_type":"editorial_import","trigger_source_ids":null,"reviewer_id":null,"review_status":"published","created_at":"2026-09-13T22:56:05.431Z"}],"secondary":[]},"methodology_version":"0.1"}