{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:DMWHJPY4PDXBXZGKUYVEDA35TM","short_pith_number":"pith:DMWHJPY4","schema_version":"1.0","canonical_sha256":"1b2c74bf1c78ee1be4caa62a41837d9b1353897bfb71d182dab3c0936716a7fb","source":{"kind":"arxiv","id":"math/0606575","version":2},"attestation_state":"computed","paper":{"title":"Nontrivial Alexander polynomials of knots and links","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Stefan Friedl, Stefano Vidussi","submitted_at":"2006-06-23T00:29:26Z","abstract_excerpt":"In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguish knots. In particular, we recast and extend by geometric means a recent result of Silver and Williams on the nontriviality of twisted Alexander polynomials for nontrivial knots. Furthermore building on results in [FV06b] we prove that these invariants decide if a genus one knot is fibered, and we also show that these invariants distinguish all mutants with up to 12 crossings."},"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/0606575","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-06-23T00:29:26Z","cross_cats_sorted":[],"title_canon_sha256":"c13ebe3fec2e104101816f60a8b813eb052e37ba30c07ffc0035d3e82d949c55","abstract_canon_sha256":"f5ff70b2810968eff707e9cd290a9d7cc9e01f797e54ce903fe0edbfaca69888"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:44.768120Z","signature_b64":"t8Khj7oqckEd0AQXXOMsjm7NfyiaAYc/JrC2F9mEyzdsTKWjmOkzPL2TgvftzKeiS01us3pe9QtQxnC+ipnKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b2c74bf1c78ee1be4caa62a41837d9b1353897bfb71d182dab3c0936716a7fb","last_reissued_at":"2026-05-17T23:57:44.767488Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:44.767488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nontrivial Alexander polynomials of knots and links","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Stefan Friedl, Stefano Vidussi","submitted_at":"2006-06-23T00:29:26Z","abstract_excerpt":"In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguish knots. In particular, we recast and extend by geometric means a recent result of Silver and Williams on the nontriviality of twisted Alexander polynomials for nontrivial knots. Furthermore building on results in [FV06b] we prove that these invariants decide if a genus one knot is fibered, and we also show that these invariants distinguish all mutants with up to 12 crossings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606575","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":""},"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/0606575","created_at":"2026-05-17T23:57:44.767585+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0606575v2","created_at":"2026-05-17T23:57:44.767585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606575","created_at":"2026-05-17T23:57:44.767585+00:00"},{"alias_kind":"pith_short_12","alias_value":"DMWHJPY4PDXB","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"DMWHJPY4PDXBXZGK","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"DMWHJPY4","created_at":"2026-05-18T12:25:53.939244+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/DMWHJPY4PDXBXZGKUYVEDA35TM","json":"https://pith.science/pith/DMWHJPY4PDXBXZGKUYVEDA35TM.json","graph_json":"https://pith.science/api/pith-number/DMWHJPY4PDXBXZGKUYVEDA35TM/graph.json","events_json":"https://pith.science/api/pith-number/DMWHJPY4PDXBXZGKUYVEDA35TM/events.json","paper":"https://pith.science/paper/DMWHJPY4"},"agent_actions":{"view_html":"https://pith.science/pith/DMWHJPY4PDXBXZGKUYVEDA35TM","download_json":"https://pith.science/pith/DMWHJPY4PDXBXZGKUYVEDA35TM.json","view_paper":"https://pith.science/paper/DMWHJPY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0606575&json=true","fetch_graph":"https://pith.science/api/pith-number/DMWHJPY4PDXBXZGKUYVEDA35TM/graph.json","fetch_events":"https://pith.science/api/pith-number/DMWHJPY4PDXBXZGKUYVEDA35TM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DMWHJPY4PDXBXZGKUYVEDA35TM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DMWHJPY4PDXBXZGKUYVEDA35TM/action/storage_attestation","attest_author":"https://pith.science/pith/DMWHJPY4PDXBXZGKUYVEDA35TM/action/author_attestation","sign_citation":"https://pith.science/pith/DMWHJPY4PDXBXZGKUYVEDA35TM/action/citation_signature","submit_replication":"https://pith.science/pith/DMWHJPY4PDXBXZGKUYVEDA35TM/action/replication_record"}},"created_at":"2026-05-17T23:57:44.767585+00:00","updated_at":"2026-05-17T23:57:44.767585+00:00"}