{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3NPXEYRFL65LG2MRLJ7EESSM7X","short_pith_number":"pith:3NPXEYRF","schema_version":"1.0","canonical_sha256":"db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e","source":{"kind":"arxiv","id":"1212.1531","version":1},"attestation_state":"computed","paper":{"title":"Computing closed essential surfaces in knot complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.GT","authors_text":"Alexander Coward, Benjamin A. Burton, Stephan Tillmann","submitted_at":"2012-12-07T05:48:05Z","abstract_excerpt":"We present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences; however, systematically testing it has until now been infeasibly slow, and current techniques only apply to specific families of knots. As a testament to its practicality, we run the algorithm over a comprehensive body of 2979 knots, including the two 20-crossing dodecahedral knots, yielding results that were not previously known.\n  The algorithm derives from the original Jaco-Oertel framework, involves both enumerati"},"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":"1212.1531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T05:48:05Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"02c79a8b67385ff56c08c14b139b34beec23770792ec5006724008f0989a036e","abstract_canon_sha256":"7868ae034aa4e745b8f54eb9119f2a6978529f7e94dba62bcd6ad1579cc6be14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:57.606196Z","signature_b64":"eTZlRb6mfa1kMjHBpyMqnZcBDk8U+10+mChb6FUFtIk2JoPp3eKvToWm2rpyIMxYKQY0TjWMKRDK/PsRsvTWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e","last_reissued_at":"2026-05-18T03:15:57.605433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:57.605433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing closed essential surfaces in knot complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.GT","authors_text":"Alexander Coward, Benjamin A. Burton, Stephan Tillmann","submitted_at":"2012-12-07T05:48:05Z","abstract_excerpt":"We present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences; however, systematically testing it has until now been infeasibly slow, and current techniques only apply to specific families of knots. As a testament to its practicality, we run the algorithm over a comprehensive body of 2979 knots, including the two 20-crossing dodecahedral knots, yielding results that were not previously known.\n  The algorithm derives from the original Jaco-Oertel framework, involves both enumerati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1531","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":"1212.1531","created_at":"2026-05-18T03:15:57.605551+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.1531v1","created_at":"2026-05-18T03:15:57.605551+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1531","created_at":"2026-05-18T03:15:57.605551+00:00"},{"alias_kind":"pith_short_12","alias_value":"3NPXEYRFL65L","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3NPXEYRFL65LG2MR","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3NPXEYRF","created_at":"2026-05-18T12:26:53.410803+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/3NPXEYRFL65LG2MRLJ7EESSM7X","json":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X.json","graph_json":"https://pith.science/api/pith-number/3NPXEYRFL65LG2MRLJ7EESSM7X/graph.json","events_json":"https://pith.science/api/pith-number/3NPXEYRFL65LG2MRLJ7EESSM7X/events.json","paper":"https://pith.science/paper/3NPXEYRF"},"agent_actions":{"view_html":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X","download_json":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X.json","view_paper":"https://pith.science/paper/3NPXEYRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.1531&json=true","fetch_graph":"https://pith.science/api/pith-number/3NPXEYRFL65LG2MRLJ7EESSM7X/graph.json","fetch_events":"https://pith.science/api/pith-number/3NPXEYRFL65LG2MRLJ7EESSM7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/action/storage_attestation","attest_author":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/action/author_attestation","sign_citation":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/action/citation_signature","submit_replication":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/action/replication_record"}},"created_at":"2026-05-18T03:15:57.605551+00:00","updated_at":"2026-05-18T03:15:57.605551+00:00"}