{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:Z6ZB3UJWMDGVYC6SG6BKCMZO36","short_pith_number":"pith:Z6ZB3UJW","schema_version":"1.0","canonical_sha256":"cfb21dd13660cd5c0bd23782a1332edfab77a10c54c2857d3247153d0bc23154","source":{"kind":"arxiv","id":"math/0502518","version":2},"attestation_state":"computed","paper":{"title":"Calculus of the first non-trivial 1-cocycle of the space of long knots","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Victor Tourtchine","submitted_at":"2005-02-24T16:05:55Z","abstract_excerpt":"For the space of long knots in R^3, Vassiliev's theory defines the so called finite order cocycles. Zero degree cocycles are finite type knot invariants. The first non-trivial cocycle of positive dimension in the space of long knots has dimension one and order three. We apply Vassiliev's combinatorial formula, and find the value mod 2 of this cocycle on the 1-cycles that are obtained by dragging knots one along the other or by rotating around a fixed line."},"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":"math/0502518","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2005-02-24T16:05:55Z","cross_cats_sorted":[],"title_canon_sha256":"2f0e3a6bd72e3c9a929656cefc788b070c4705eef24670fbe1b7db973a994f55","abstract_canon_sha256":"55249831bcfa89b7df78fc157f9ba37291b0680682c71561db465fb49642d347"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:44.868407Z","signature_b64":"CuVhlWIdezHkYEhs72C53dE3MtnQvQg5MHDpJL9xtMpafaBdn4f+NbOsGK5IN2LOhBAKSGqk4q5omPDGGE4bCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfb21dd13660cd5c0bd23782a1332edfab77a10c54c2857d3247153d0bc23154","last_reissued_at":"2026-07-04T14:39:44.868053Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:44.868053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Calculus of the first non-trivial 1-cocycle of the space of long knots","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Victor Tourtchine","submitted_at":"2005-02-24T16:05:55Z","abstract_excerpt":"For the space of long knots in R^3, Vassiliev's theory defines the so called finite order cocycles. Zero degree cocycles are finite type knot invariants. The first non-trivial cocycle of positive dimension in the space of long knots has dimension one and order three. We apply Vassiliev's combinatorial formula, and find the value mod 2 of this cocycle on the 1-cycles that are obtained by dragging knots one along the other or by rotating around a fixed line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502518","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0502518/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0502518","created_at":"2026-07-04T14:39:44.868113+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0502518v2","created_at":"2026-07-04T14:39:44.868113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502518","created_at":"2026-07-04T14:39:44.868113+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z6ZB3UJWMDGV","created_at":"2026-07-04T14:39:44.868113+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z6ZB3UJWMDGVYC6S","created_at":"2026-07-04T14:39:44.868113+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z6ZB3UJW","created_at":"2026-07-04T14:39:44.868113+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.22958","citing_title":"A Fox-Neuwirth Basis for the Sinha Spectral Sequence","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36","json":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36.json","graph_json":"https://pith.science/api/pith-number/Z6ZB3UJWMDGVYC6SG6BKCMZO36/graph.json","events_json":"https://pith.science/api/pith-number/Z6ZB3UJWMDGVYC6SG6BKCMZO36/events.json","paper":"https://pith.science/paper/Z6ZB3UJW"},"agent_actions":{"view_html":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36","download_json":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36.json","view_paper":"https://pith.science/paper/Z6ZB3UJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0502518&json=true","fetch_graph":"https://pith.science/api/pith-number/Z6ZB3UJWMDGVYC6SG6BKCMZO36/graph.json","fetch_events":"https://pith.science/api/pith-number/Z6ZB3UJWMDGVYC6SG6BKCMZO36/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36/action/storage_attestation","attest_author":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36/action/author_attestation","sign_citation":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36/action/citation_signature","submit_replication":"https://pith.science/pith/Z6ZB3UJWMDGVYC6SG6BKCMZO36/action/replication_record"}},"created_at":"2026-07-04T14:39:44.868113+00:00","updated_at":"2026-07-04T14:39:44.868113+00:00"}