{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:E2B47J25272HX5A3ILXMIWH6FT","short_pith_number":"pith:E2B47J25","schema_version":"1.0","canonical_sha256":"2683cfa75dd7f47bf41b42eec458fe2ce59c372478d1fbb1ff4f99e75cc96bc7","source":{"kind":"arxiv","id":"1102.5730","version":1},"attestation_state":"computed","paper":{"title":"Knot concordance and homology cobordism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bridget D. Franklin, Matthew Hedden, Peter D. Horn, Tim D. Cochran","submitted_at":"2011-02-28T18:34:19Z","abstract_excerpt":"We consider the question: \"If the zero-framed surgeries on two oriented knots in the 3-sphere are integral homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?\" We show that this question has a negative answer in the smooth category, even for topologically slice knots. To show this we first prove that the zero-framed surgery on K is Z-homology cobordant to the zero-framed surgery on many of its winding number one satellites P(K). Then we prove that in many cases the tau and s-invariants of K and P(K) differ. Consequently neither tau "},"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":"1102.5730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-02-28T18:34:19Z","cross_cats_sorted":[],"title_canon_sha256":"a5dd9458f15b71b23a2cd933654a5522ee9d3a9d61d45153caeda7b2d55fe6be","abstract_canon_sha256":"d43b0924125a2e8260cf7749ef4db0478f29a75b2b4430d013463d0654764122"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:03.198646Z","signature_b64":"gFrdf/5RoXQDOSd5cv+vJp/w+5759UfW5tBa8DwXBRFq6jD47qtNMa87w4gi+kWb6EsSSiQy3nXYGt76NurTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2683cfa75dd7f47bf41b42eec458fe2ce59c372478d1fbb1ff4f99e75cc96bc7","last_reissued_at":"2026-05-18T03:30:03.197876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:03.197876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Knot concordance and homology cobordism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bridget D. Franklin, Matthew Hedden, Peter D. Horn, Tim D. Cochran","submitted_at":"2011-02-28T18:34:19Z","abstract_excerpt":"We consider the question: \"If the zero-framed surgeries on two oriented knots in the 3-sphere are integral homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?\" We show that this question has a negative answer in the smooth category, even for topologically slice knots. To show this we first prove that the zero-framed surgery on K is Z-homology cobordant to the zero-framed surgery on many of its winding number one satellites P(K). Then we prove that in many cases the tau and s-invariants of K and P(K) differ. Consequently neither tau "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5730","kind":"arxiv","version":1},"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":"1102.5730","created_at":"2026-05-18T03:30:03.197997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.5730v1","created_at":"2026-05-18T03:30:03.197997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5730","created_at":"2026-05-18T03:30:03.197997+00:00"},{"alias_kind":"pith_short_12","alias_value":"E2B47J25272H","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"E2B47J25272HX5A3","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"E2B47J25","created_at":"2026-05-18T12:26:26.731475+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/E2B47J25272HX5A3ILXMIWH6FT","json":"https://pith.science/pith/E2B47J25272HX5A3ILXMIWH6FT.json","graph_json":"https://pith.science/api/pith-number/E2B47J25272HX5A3ILXMIWH6FT/graph.json","events_json":"https://pith.science/api/pith-number/E2B47J25272HX5A3ILXMIWH6FT/events.json","paper":"https://pith.science/paper/E2B47J25"},"agent_actions":{"view_html":"https://pith.science/pith/E2B47J25272HX5A3ILXMIWH6FT","download_json":"https://pith.science/pith/E2B47J25272HX5A3ILXMIWH6FT.json","view_paper":"https://pith.science/paper/E2B47J25","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.5730&json=true","fetch_graph":"https://pith.science/api/pith-number/E2B47J25272HX5A3ILXMIWH6FT/graph.json","fetch_events":"https://pith.science/api/pith-number/E2B47J25272HX5A3ILXMIWH6FT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E2B47J25272HX5A3ILXMIWH6FT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E2B47J25272HX5A3ILXMIWH6FT/action/storage_attestation","attest_author":"https://pith.science/pith/E2B47J25272HX5A3ILXMIWH6FT/action/author_attestation","sign_citation":"https://pith.science/pith/E2B47J25272HX5A3ILXMIWH6FT/action/citation_signature","submit_replication":"https://pith.science/pith/E2B47J25272HX5A3ILXMIWH6FT/action/replication_record"}},"created_at":"2026-05-18T03:30:03.197997+00:00","updated_at":"2026-05-18T03:30:03.197997+00:00"}