{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:LMWULXLS25ML5KBETZCEUW6Y5X","short_pith_number":"pith:LMWULXLS","schema_version":"1.0","canonical_sha256":"5b2d45dd72d758bea8249e444a5bd8edc2554f2069d4016e6523cf33e2376571","source":{"kind":"arxiv","id":"math/0307328","version":1},"attestation_state":"computed","paper":{"title":"Alexander polynomials of non-locally-flat knots","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Greg Friedman","submitted_at":"2003-07-24T22:33:23Z","abstract_excerpt":"We generalize the classical study of Alexander polynomials of smooth or PL locally-flat knots to PL knots that are not necessarily locally-flat. We introduce three families of generalized Alexander polynomials and study their properties. For knots with point singularities, we obtain a classification of these polynomials that is complete except for one special low-dimensional case. This classification extends existing classifications for PL locally-flat knots. For knots with higher-dimensional singularities, we further extend the necessary conditions on the invariants. We also construct several"},"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/0307328","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2003-07-24T22:33:23Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f6ff591dd92b4e8e192eb16e1e3a80323240ffeb9c36e8b7ceec3346725578e2","abstract_canon_sha256":"e7dcef61113ae979e63dcdbbe4beb6b753d29c0640c1e04117273c5fdfe99371"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:26.477930Z","signature_b64":"vfdJMJQp34e6xFZA/3O6YgeuvzeEmiZowyIx3RZBjHXOmRCLmqZsgvN9wwvdYprvviXxnVb6TnvoID2wHFAAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b2d45dd72d758bea8249e444a5bd8edc2554f2069d4016e6523cf33e2376571","last_reissued_at":"2026-05-18T04:25:26.476993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:26.476993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Alexander polynomials of non-locally-flat knots","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Greg Friedman","submitted_at":"2003-07-24T22:33:23Z","abstract_excerpt":"We generalize the classical study of Alexander polynomials of smooth or PL locally-flat knots to PL knots that are not necessarily locally-flat. We introduce three families of generalized Alexander polynomials and study their properties. For knots with point singularities, we obtain a classification of these polynomials that is complete except for one special low-dimensional case. This classification extends existing classifications for PL locally-flat knots. For knots with higher-dimensional singularities, we further extend the necessary conditions on the invariants. We also construct several"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307328","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":"math/0307328","created_at":"2026-05-18T04:25:26.477128+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0307328v1","created_at":"2026-05-18T04:25:26.477128+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307328","created_at":"2026-05-18T04:25:26.477128+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMWULXLS25ML","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMWULXLS25ML5KBE","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMWULXLS","created_at":"2026-05-18T12:25:52.051335+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/LMWULXLS25ML5KBETZCEUW6Y5X","json":"https://pith.science/pith/LMWULXLS25ML5KBETZCEUW6Y5X.json","graph_json":"https://pith.science/api/pith-number/LMWULXLS25ML5KBETZCEUW6Y5X/graph.json","events_json":"https://pith.science/api/pith-number/LMWULXLS25ML5KBETZCEUW6Y5X/events.json","paper":"https://pith.science/paper/LMWULXLS"},"agent_actions":{"view_html":"https://pith.science/pith/LMWULXLS25ML5KBETZCEUW6Y5X","download_json":"https://pith.science/pith/LMWULXLS25ML5KBETZCEUW6Y5X.json","view_paper":"https://pith.science/paper/LMWULXLS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0307328&json=true","fetch_graph":"https://pith.science/api/pith-number/LMWULXLS25ML5KBETZCEUW6Y5X/graph.json","fetch_events":"https://pith.science/api/pith-number/LMWULXLS25ML5KBETZCEUW6Y5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMWULXLS25ML5KBETZCEUW6Y5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMWULXLS25ML5KBETZCEUW6Y5X/action/storage_attestation","attest_author":"https://pith.science/pith/LMWULXLS25ML5KBETZCEUW6Y5X/action/author_attestation","sign_citation":"https://pith.science/pith/LMWULXLS25ML5KBETZCEUW6Y5X/action/citation_signature","submit_replication":"https://pith.science/pith/LMWULXLS25ML5KBETZCEUW6Y5X/action/replication_record"}},"created_at":"2026-05-18T04:25:26.477128+00:00","updated_at":"2026-05-18T04:25:26.477128+00:00"}