{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:34QHLEMXVNOZRYQFE2ECL3CFEW","short_pith_number":"pith:34QHLEMX","schema_version":"1.0","canonical_sha256":"df20759197ab5d98e205268825ec4525bf7f95943e31b841ed0cdc4b7c4ff71d","source":{"kind":"arxiv","id":"1303.4418","version":2},"attestation_state":"computed","paper":{"title":"Counterexamples to Kauffman's Conjectures on Slice Knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christopher William Davis, Tim D. Cochran","submitted_at":"2013-03-18T20:43:54Z","abstract_excerpt":"In 1982 Louis Kauffman conjectured that if a knot in the 3-sphere is a slice knot then on any Seifert surface for that knot there exists a homologically essential simple closed curve of self-linking zero which is itself a slice knot, or at least has Arf invariant zero. Since that time, considerable evidence has been amassed in support of this conjecture. In particular, many invariants that obstruct a knot from being a slice knot have been explictly expressed in terms of invariants of such curves on the Seifert surface. We give counterexamples to Kauffman's conjecture, that is, we exhibit (smoo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.4418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-18T20:43:54Z","cross_cats_sorted":[],"title_canon_sha256":"618db0d7ee5efaec521f7365f31ad2fdb8fd6999c4f6b051f1b68d61ccf6d856","abstract_canon_sha256":"50445c68ca68c2c54f586aa8cb5b89467ab72cc6a4ccc512af4f3714583d1833"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:44.306010Z","signature_b64":"QfRCGrnFRDT47YKG275R4pO8Y88RYd1aohVR51ECaU3LeKUGyPCedkn8lT3rQ0TqaDdhPXbZBieTOETgeqooDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df20759197ab5d98e205268825ec4525bf7f95943e31b841ed0cdc4b7c4ff71d","last_reissued_at":"2026-05-18T02:56:44.305509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:44.305509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counterexamples to Kauffman's Conjectures on Slice Knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christopher William Davis, Tim D. Cochran","submitted_at":"2013-03-18T20:43:54Z","abstract_excerpt":"In 1982 Louis Kauffman conjectured that if a knot in the 3-sphere is a slice knot then on any Seifert surface for that knot there exists a homologically essential simple closed curve of self-linking zero which is itself a slice knot, or at least has Arf invariant zero. Since that time, considerable evidence has been amassed in support of this conjecture. In particular, many invariants that obstruct a knot from being a slice knot have been explictly expressed in terms of invariants of such curves on the Seifert surface. We give counterexamples to Kauffman's conjecture, that is, we exhibit (smoo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4418","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.4418","created_at":"2026-05-18T02:56:44.305595+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.4418v2","created_at":"2026-05-18T02:56:44.305595+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4418","created_at":"2026-05-18T02:56:44.305595+00:00"},{"alias_kind":"pith_short_12","alias_value":"34QHLEMXVNOZ","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"34QHLEMXVNOZRYQF","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"34QHLEMX","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW","json":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW.json","graph_json":"https://pith.science/api/pith-number/34QHLEMXVNOZRYQFE2ECL3CFEW/graph.json","events_json":"https://pith.science/api/pith-number/34QHLEMXVNOZRYQFE2ECL3CFEW/events.json","paper":"https://pith.science/paper/34QHLEMX"},"agent_actions":{"view_html":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW","download_json":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW.json","view_paper":"https://pith.science/paper/34QHLEMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.4418&json=true","fetch_graph":"https://pith.science/api/pith-number/34QHLEMXVNOZRYQFE2ECL3CFEW/graph.json","fetch_events":"https://pith.science/api/pith-number/34QHLEMXVNOZRYQFE2ECL3CFEW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW/action/storage_attestation","attest_author":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW/action/author_attestation","sign_citation":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW/action/citation_signature","submit_replication":"https://pith.science/pith/34QHLEMXVNOZRYQFE2ECL3CFEW/action/replication_record"}},"created_at":"2026-05-18T02:56:44.305595+00:00","updated_at":"2026-05-18T02:56:44.305595+00:00"}