{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3Y4L4A7CCTGZM54YYOAEXJUJNQ","short_pith_number":"pith:3Y4L4A7C","schema_version":"1.0","canonical_sha256":"de38be03e214cd967798c3804ba6896c26c61ce676c69847b4d6b0b5effe7728","source":{"kind":"arxiv","id":"1802.08899","version":1},"attestation_state":"computed","paper":{"title":"Longitudinal Mapping Knot Invariant for SU(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Masahico Saito, W. Edwin Clark","submitted_at":"2018-02-24T19:24:48Z","abstract_excerpt":"The knot coloring polynomial defined by Eisermann for a finite pointed group is generalized to an infinite pointed group as the longitudinal mapping invariant of a knot. In turn this can be thought of as a generalization of the quandle 2-cocycle invariant for finite quandles. If the group is a topological group then this invariant can be thought of a topological generalization of the 2-cocycle invariant. The longitudinal mapping invariant is based on a meridian-longitude pair in the knot group. We also give an interpretation of the invariant in terms of quandle colorings of a 1-tangle for gene"},"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":"1802.08899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-02-24T19:24:48Z","cross_cats_sorted":[],"title_canon_sha256":"121287df6ed1fc3d0919de064fa9334111e91013c5de8ddc1c28454d8039848c","abstract_canon_sha256":"aa2b54c47b366392e6dbb58c0650327af036870fa154f690c574598b792328cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:36.113101Z","signature_b64":"TJZ1sQI1M1OgHaQKX9ZuN1VaXigsUxkxLf4I2mj5SV0GVpEpAie+igSN3o1VjBxotan08q/57/SgewuJslPPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de38be03e214cd967798c3804ba6896c26c61ce676c69847b4d6b0b5effe7728","last_reissued_at":"2026-05-18T00:22:36.112431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:36.112431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Longitudinal Mapping Knot Invariant for SU(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Masahico Saito, W. Edwin Clark","submitted_at":"2018-02-24T19:24:48Z","abstract_excerpt":"The knot coloring polynomial defined by Eisermann for a finite pointed group is generalized to an infinite pointed group as the longitudinal mapping invariant of a knot. In turn this can be thought of as a generalization of the quandle 2-cocycle invariant for finite quandles. If the group is a topological group then this invariant can be thought of a topological generalization of the 2-cocycle invariant. The longitudinal mapping invariant is based on a meridian-longitude pair in the knot group. We also give an interpretation of the invariant in terms of quandle colorings of a 1-tangle for gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08899","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":"1802.08899","created_at":"2026-05-18T00:22:36.112530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.08899v1","created_at":"2026-05-18T00:22:36.112530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08899","created_at":"2026-05-18T00:22:36.112530+00:00"},{"alias_kind":"pith_short_12","alias_value":"3Y4L4A7CCTGZ","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"3Y4L4A7CCTGZM54Y","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"3Y4L4A7C","created_at":"2026-05-18T12:32:05.422762+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/3Y4L4A7CCTGZM54YYOAEXJUJNQ","json":"https://pith.science/pith/3Y4L4A7CCTGZM54YYOAEXJUJNQ.json","graph_json":"https://pith.science/api/pith-number/3Y4L4A7CCTGZM54YYOAEXJUJNQ/graph.json","events_json":"https://pith.science/api/pith-number/3Y4L4A7CCTGZM54YYOAEXJUJNQ/events.json","paper":"https://pith.science/paper/3Y4L4A7C"},"agent_actions":{"view_html":"https://pith.science/pith/3Y4L4A7CCTGZM54YYOAEXJUJNQ","download_json":"https://pith.science/pith/3Y4L4A7CCTGZM54YYOAEXJUJNQ.json","view_paper":"https://pith.science/paper/3Y4L4A7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.08899&json=true","fetch_graph":"https://pith.science/api/pith-number/3Y4L4A7CCTGZM54YYOAEXJUJNQ/graph.json","fetch_events":"https://pith.science/api/pith-number/3Y4L4A7CCTGZM54YYOAEXJUJNQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3Y4L4A7CCTGZM54YYOAEXJUJNQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3Y4L4A7CCTGZM54YYOAEXJUJNQ/action/storage_attestation","attest_author":"https://pith.science/pith/3Y4L4A7CCTGZM54YYOAEXJUJNQ/action/author_attestation","sign_citation":"https://pith.science/pith/3Y4L4A7CCTGZM54YYOAEXJUJNQ/action/citation_signature","submit_replication":"https://pith.science/pith/3Y4L4A7CCTGZM54YYOAEXJUJNQ/action/replication_record"}},"created_at":"2026-05-18T00:22:36.112530+00:00","updated_at":"2026-05-18T00:22:36.112530+00:00"}