{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3M42KJHNVTS7ZXIGRFG4NUWI3Z","short_pith_number":"pith:3M42KJHN","schema_version":"1.0","canonical_sha256":"db39a524edace5fcdd06894dc6d2c8de555326cd37e67304bb2d48b040fde029","source":{"kind":"arxiv","id":"1210.5722","version":3},"attestation_state":"computed","paper":{"title":"Transverse string topology and the cord algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.GT","authors_text":"Dennis Sullivan, Jason McGibbon, Michael Sullivan, Somnath Basu","submitted_at":"2012-10-21T12:30:27Z","abstract_excerpt":"We define a coalgebra structure for open strings transverse to any framed codimension 2 submanifold. When the submanifold is a knot in R^3, we show this structure recovers a specialization of the Ng cord algebra, a non-trivial knot invariant which is not determined by a number of other knot invariants."},"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":"1210.5722","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-21T12:30:27Z","cross_cats_sorted":["math.AT","math.SG"],"title_canon_sha256":"fc7f2f94ab2182032659ff6f76c888fbd3804ab9c50606bf2893506374ffcc05","abstract_canon_sha256":"19e86dd77b6d504db4021f5972f721776e362ee368ed3ed6065c6e1ecec2ba3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:45.698237Z","signature_b64":"wptCY9HFEJjtDgjthAyCaQTZY+pGOlUzgvlIbKPJSDSkA+wfdzptpXh0X8RHjZx/E+mvKZ705unmfzxt+RU6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db39a524edace5fcdd06894dc6d2c8de555326cd37e67304bb2d48b040fde029","last_reissued_at":"2026-05-18T01:23:45.697376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:45.697376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transverse string topology and the cord algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.GT","authors_text":"Dennis Sullivan, Jason McGibbon, Michael Sullivan, Somnath Basu","submitted_at":"2012-10-21T12:30:27Z","abstract_excerpt":"We define a coalgebra structure for open strings transverse to any framed codimension 2 submanifold. When the submanifold is a knot in R^3, we show this structure recovers a specialization of the Ng cord algebra, a non-trivial knot invariant which is not determined by a number of other knot invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5722","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":"1210.5722","created_at":"2026-05-18T01:23:45.697512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.5722v3","created_at":"2026-05-18T01:23:45.697512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5722","created_at":"2026-05-18T01:23:45.697512+00:00"},{"alias_kind":"pith_short_12","alias_value":"3M42KJHNVTS7","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"3M42KJHNVTS7ZXIG","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"3M42KJHN","created_at":"2026-05-18T12:26:50.516681+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/3M42KJHNVTS7ZXIGRFG4NUWI3Z","json":"https://pith.science/pith/3M42KJHNVTS7ZXIGRFG4NUWI3Z.json","graph_json":"https://pith.science/api/pith-number/3M42KJHNVTS7ZXIGRFG4NUWI3Z/graph.json","events_json":"https://pith.science/api/pith-number/3M42KJHNVTS7ZXIGRFG4NUWI3Z/events.json","paper":"https://pith.science/paper/3M42KJHN"},"agent_actions":{"view_html":"https://pith.science/pith/3M42KJHNVTS7ZXIGRFG4NUWI3Z","download_json":"https://pith.science/pith/3M42KJHNVTS7ZXIGRFG4NUWI3Z.json","view_paper":"https://pith.science/paper/3M42KJHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.5722&json=true","fetch_graph":"https://pith.science/api/pith-number/3M42KJHNVTS7ZXIGRFG4NUWI3Z/graph.json","fetch_events":"https://pith.science/api/pith-number/3M42KJHNVTS7ZXIGRFG4NUWI3Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3M42KJHNVTS7ZXIGRFG4NUWI3Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3M42KJHNVTS7ZXIGRFG4NUWI3Z/action/storage_attestation","attest_author":"https://pith.science/pith/3M42KJHNVTS7ZXIGRFG4NUWI3Z/action/author_attestation","sign_citation":"https://pith.science/pith/3M42KJHNVTS7ZXIGRFG4NUWI3Z/action/citation_signature","submit_replication":"https://pith.science/pith/3M42KJHNVTS7ZXIGRFG4NUWI3Z/action/replication_record"}},"created_at":"2026-05-18T01:23:45.697512+00:00","updated_at":"2026-05-18T01:23:45.697512+00:00"}