{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:NB6XALQQCD32CJOO3D2RTYUHQZ","short_pith_number":"pith:NB6XALQQ","schema_version":"1.0","canonical_sha256":"687d702e1010f7a125ced8f519e2878665311c409b4433aca54a6b01e89eb041","source":{"kind":"arxiv","id":"2110.03082","version":4},"attestation_state":"computed","paper":{"title":"The Jones Polynomial from a Goeritz Matrix","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Joe Boninger","submitted_at":"2021-10-06T22:03:26Z","abstract_excerpt":"We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from a Goeritz matrix for that link. Further, we show how the Jones polynomial can be recovered from a Goeritz matrix when the corresponding checkerboard surface is orientable, or when more information is known about its Gordon-Litherland form. In the process we develop a theory of Goeritz matrices for cographic matroids, which extends the bracket polynomial to any symmetric integer matrix. We place this work in the context of links in thickened surfaces."},"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":"2110.03082","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2021-10-06T22:03:26Z","cross_cats_sorted":[],"title_canon_sha256":"fbf24a5aeb6899fd285c772949afa4d46271be381504438e101525d5b2499bbb","abstract_canon_sha256":"e7059a618dcf850757c45ad2baf16b45c3733fa92c05c49814f7280225a102a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:24:16.873502Z","signature_b64":"8kKimfA9tyfNw6Y5u8ks3PK/Z04unBwsIlLJjuq7l+QXpNOeCRWPM2IcrhQwfsXJDnB9Xkt3PXnIXse4XCapCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"687d702e1010f7a125ced8f519e2878665311c409b4433aca54a6b01e89eb041","last_reissued_at":"2026-07-05T10:24:16.872649Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:24:16.872649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Jones Polynomial from a Goeritz Matrix","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Joe Boninger","submitted_at":"2021-10-06T22:03:26Z","abstract_excerpt":"We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from a Goeritz matrix for that link. Further, we show how the Jones polynomial can be recovered from a Goeritz matrix when the corresponding checkerboard surface is orientable, or when more information is known about its Gordon-Litherland form. In the process we develop a theory of Goeritz matrices for cographic matroids, which extends the bracket polynomial to any symmetric integer matrix. We place this work in the context of links in thickened surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.03082","kind":"arxiv","version":4},"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/2110.03082/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":"2110.03082","created_at":"2026-07-05T10:24:16.872742+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.03082v4","created_at":"2026-07-05T10:24:16.872742+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.03082","created_at":"2026-07-05T10:24:16.872742+00:00"},{"alias_kind":"pith_short_12","alias_value":"NB6XALQQCD32","created_at":"2026-07-05T10:24:16.872742+00:00"},{"alias_kind":"pith_short_16","alias_value":"NB6XALQQCD32CJOO","created_at":"2026-07-05T10:24:16.872742+00:00"},{"alias_kind":"pith_short_8","alias_value":"NB6XALQQ","created_at":"2026-07-05T10:24:16.872742+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2507.03116","citing_title":"Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ","json":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ.json","graph_json":"https://pith.science/api/pith-number/NB6XALQQCD32CJOO3D2RTYUHQZ/graph.json","events_json":"https://pith.science/api/pith-number/NB6XALQQCD32CJOO3D2RTYUHQZ/events.json","paper":"https://pith.science/paper/NB6XALQQ"},"agent_actions":{"view_html":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ","download_json":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ.json","view_paper":"https://pith.science/paper/NB6XALQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.03082&json=true","fetch_graph":"https://pith.science/api/pith-number/NB6XALQQCD32CJOO3D2RTYUHQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/NB6XALQQCD32CJOO3D2RTYUHQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ/action/storage_attestation","attest_author":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ/action/author_attestation","sign_citation":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ/action/citation_signature","submit_replication":"https://pith.science/pith/NB6XALQQCD32CJOO3D2RTYUHQZ/action/replication_record"}},"created_at":"2026-07-05T10:24:16.872742+00:00","updated_at":"2026-07-05T10:24:16.872742+00:00"}