{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DPVNL72EUT5MWRKZUNNACNCLLI","short_pith_number":"pith:DPVNL72E","schema_version":"1.0","canonical_sha256":"1bead5ff44a4facb4559a35a01344b5a1abdbddf8797c27dce687111081e8d15","source":{"kind":"arxiv","id":"1409.7032","version":3},"attestation_state":"computed","paper":{"title":"On the Alexander polynomial of lens space knot","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Motoo Tange","submitted_at":"2014-09-24T18:08:41Z","abstract_excerpt":"Ozsv\\'ath-Szab\\'o proved the property that any coefficient of Alexander polynomial of lens space knot is either $\\pm1$ or $0$ and the non-zero coefficients are alternating. Combining the formulas of the Alexander polynomial of lens space knots due to Kadokami-Yamada and Ichihara-Saito-Teragaito, we refine Ozsv\\'ath-Szab\\'o's property as the existence of simple curves included in a region in ${\\Bbb R}^2$. The existence of curves, that has no end-points connected, is just 1-component in a region, can search distribution of non-zero coefficients of the Alexander polynomial of the lens space knot."},"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":"1409.7032","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-24T18:08:41Z","cross_cats_sorted":[],"title_canon_sha256":"a8d5bd547529aa8879f0c7a93c880e493a412845e62dd3a5e6932ce9474d6d3f","abstract_canon_sha256":"8e5b6a71a11926e7e80c8dccb82aad795e0d6b10b8f32efd33d7f8c1e62f0c7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:53.872144Z","signature_b64":"/GiucuPiKbM5QXCC0PxVPVYJ7vfwTDsCpSAemu7bwch8ugKXddm0ZbOss40NsTPLJwB7xhKC/Bm9lWYYbD8JCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bead5ff44a4facb4559a35a01344b5a1abdbddf8797c27dce687111081e8d15","last_reissued_at":"2026-05-18T00:13:53.871436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:53.871436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Alexander polynomial of lens space knot","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Motoo Tange","submitted_at":"2014-09-24T18:08:41Z","abstract_excerpt":"Ozsv\\'ath-Szab\\'o proved the property that any coefficient of Alexander polynomial of lens space knot is either $\\pm1$ or $0$ and the non-zero coefficients are alternating. Combining the formulas of the Alexander polynomial of lens space knots due to Kadokami-Yamada and Ichihara-Saito-Teragaito, we refine Ozsv\\'ath-Szab\\'o's property as the existence of simple curves included in a region in ${\\Bbb R}^2$. The existence of curves, that has no end-points connected, is just 1-component in a region, can search distribution of non-zero coefficients of the Alexander polynomial of the lens space knot."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7032","kind":"arxiv","version":3},"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":"1409.7032","created_at":"2026-05-18T00:13:53.871539+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.7032v3","created_at":"2026-05-18T00:13:53.871539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7032","created_at":"2026-05-18T00:13:53.871539+00:00"},{"alias_kind":"pith_short_12","alias_value":"DPVNL72EUT5M","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DPVNL72EUT5MWRKZ","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DPVNL72E","created_at":"2026-05-18T12:28:25.294606+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/DPVNL72EUT5MWRKZUNNACNCLLI","json":"https://pith.science/pith/DPVNL72EUT5MWRKZUNNACNCLLI.json","graph_json":"https://pith.science/api/pith-number/DPVNL72EUT5MWRKZUNNACNCLLI/graph.json","events_json":"https://pith.science/api/pith-number/DPVNL72EUT5MWRKZUNNACNCLLI/events.json","paper":"https://pith.science/paper/DPVNL72E"},"agent_actions":{"view_html":"https://pith.science/pith/DPVNL72EUT5MWRKZUNNACNCLLI","download_json":"https://pith.science/pith/DPVNL72EUT5MWRKZUNNACNCLLI.json","view_paper":"https://pith.science/paper/DPVNL72E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.7032&json=true","fetch_graph":"https://pith.science/api/pith-number/DPVNL72EUT5MWRKZUNNACNCLLI/graph.json","fetch_events":"https://pith.science/api/pith-number/DPVNL72EUT5MWRKZUNNACNCLLI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DPVNL72EUT5MWRKZUNNACNCLLI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DPVNL72EUT5MWRKZUNNACNCLLI/action/storage_attestation","attest_author":"https://pith.science/pith/DPVNL72EUT5MWRKZUNNACNCLLI/action/author_attestation","sign_citation":"https://pith.science/pith/DPVNL72EUT5MWRKZUNNACNCLLI/action/citation_signature","submit_replication":"https://pith.science/pith/DPVNL72EUT5MWRKZUNNACNCLLI/action/replication_record"}},"created_at":"2026-05-18T00:13:53.871539+00:00","updated_at":"2026-05-18T00:13:53.871539+00:00"}