{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:Y6PTY3DKGY5W7WMJUFZRIUG5P6","short_pith_number":"pith:Y6PTY3DK","schema_version":"1.0","canonical_sha256":"c79f3c6c6a363b6fd989a1731450dd7f861c3e90674acc0f7207d62bafce0714","source":{"kind":"arxiv","id":"0710.3082","version":3},"attestation_state":"computed","paper":{"title":"Knot Concordance and Higher-Order Blanchfield Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Constance Leidy, Shelly Harvey, Tim D. Cochran","submitted_at":"2007-10-16T15:10:05Z","abstract_excerpt":"In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration {F_n} of the classical knot concordance group C. The filtration is important because of its strong connection to the classification of topological 4-manifolds. Here we introduce new techniques for studying C and use them to prove that, for each natural number n, the abelian group F_n/F_{n.5} has infinite rank. We establish the same result for the corresponding filtration of the smooth concordance group. We also resolve a long-standing question as to whether certain natural families of knots, first considered by Casson-Gordon and"},"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":"0710.3082","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-10-16T15:10:05Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"0bf0ad0161a1855771665995525681fd791aa712e55118fc1251e77b8bb06d88","abstract_canon_sha256":"4f84e1f4e537b3822c546815a49ca8447b40dbf1fb6c613e6f76dddba6f4c99b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:19.364016Z","signature_b64":"UNoyfj0x88Mrw9l5vI5fHd1KTmaOI+IoTVAOXMPOL2tRuGO4SIpvIO9sk4+7Y7oG1e/B7AfMjVH0Zpr00kTEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c79f3c6c6a363b6fd989a1731450dd7f861c3e90674acc0f7207d62bafce0714","last_reissued_at":"2026-05-18T02:38:19.363429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:19.363429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Knot Concordance and Higher-Order Blanchfield Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Constance Leidy, Shelly Harvey, Tim D. Cochran","submitted_at":"2007-10-16T15:10:05Z","abstract_excerpt":"In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration {F_n} of the classical knot concordance group C. The filtration is important because of its strong connection to the classification of topological 4-manifolds. Here we introduce new techniques for studying C and use them to prove that, for each natural number n, the abelian group F_n/F_{n.5} has infinite rank. We establish the same result for the corresponding filtration of the smooth concordance group. We also resolve a long-standing question as to whether certain natural families of knots, first considered by Casson-Gordon and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3082","kind":"arxiv","version":3},"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":"0710.3082","created_at":"2026-05-18T02:38:19.363507+00:00"},{"alias_kind":"arxiv_version","alias_value":"0710.3082v3","created_at":"2026-05-18T02:38:19.363507+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3082","created_at":"2026-05-18T02:38:19.363507+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y6PTY3DKGY5W","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y6PTY3DKGY5W7WMJ","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y6PTY3DK","created_at":"2026-05-18T12:25:56.245647+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/Y6PTY3DKGY5W7WMJUFZRIUG5P6","json":"https://pith.science/pith/Y6PTY3DKGY5W7WMJUFZRIUG5P6.json","graph_json":"https://pith.science/api/pith-number/Y6PTY3DKGY5W7WMJUFZRIUG5P6/graph.json","events_json":"https://pith.science/api/pith-number/Y6PTY3DKGY5W7WMJUFZRIUG5P6/events.json","paper":"https://pith.science/paper/Y6PTY3DK"},"agent_actions":{"view_html":"https://pith.science/pith/Y6PTY3DKGY5W7WMJUFZRIUG5P6","download_json":"https://pith.science/pith/Y6PTY3DKGY5W7WMJUFZRIUG5P6.json","view_paper":"https://pith.science/paper/Y6PTY3DK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0710.3082&json=true","fetch_graph":"https://pith.science/api/pith-number/Y6PTY3DKGY5W7WMJUFZRIUG5P6/graph.json","fetch_events":"https://pith.science/api/pith-number/Y6PTY3DKGY5W7WMJUFZRIUG5P6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y6PTY3DKGY5W7WMJUFZRIUG5P6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y6PTY3DKGY5W7WMJUFZRIUG5P6/action/storage_attestation","attest_author":"https://pith.science/pith/Y6PTY3DKGY5W7WMJUFZRIUG5P6/action/author_attestation","sign_citation":"https://pith.science/pith/Y6PTY3DKGY5W7WMJUFZRIUG5P6/action/citation_signature","submit_replication":"https://pith.science/pith/Y6PTY3DKGY5W7WMJUFZRIUG5P6/action/replication_record"}},"created_at":"2026-05-18T02:38:19.363507+00:00","updated_at":"2026-05-18T02:38:19.363507+00:00"}