{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6PCBVUPPRLOBDMZL7MONS6FVRN","short_pith_number":"pith:6PCBVUPP","schema_version":"1.0","canonical_sha256":"f3c41ad1ef8adc11b32bfb1cd978b58b73abae3fbbda00891c8ce32bddf174d4","source":{"kind":"arxiv","id":"1411.7915","version":4},"attestation_state":"computed","paper":{"title":"Geometrically and diagrammatically maximal knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Abhijit Champanerkar, Ilya Kofman, Jessica S. Purcell","submitted_at":"2014-11-28T15:47:54Z","abstract_excerpt":"The ratio of volume to crossing number of a hyperbolic knot is known to be bounded above by the volume of a regular ideal octahedron, and a similar bound is conjectured for the knot determinant per crossing. We investigate a natural question motivated by these bounds: For which knots are these ratios nearly maximal? We show that many families of alternating knots and links simultaneously maximize both ratios."},"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":"1411.7915","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-28T15:47:54Z","cross_cats_sorted":[],"title_canon_sha256":"ea8072d9286bbb4689d40f70f5bc837c6198a86b8594537713c4761353f0710b","abstract_canon_sha256":"ca51b1eaee2efe10c15190c00a5635b0d892c21da034535de0abcaa080d498ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:41.680789Z","signature_b64":"vNX6WgkiUyX5tK/70MAiNQee6ktk1x3P+INFZTdtUgqYvj3goNJllWHYNsJhxjwfOGmT0UnZyYm3h+K6+574Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3c41ad1ef8adc11b32bfb1cd978b58b73abae3fbbda00891c8ce32bddf174d4","last_reissued_at":"2026-05-18T00:00:41.680383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:41.680383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometrically and diagrammatically maximal knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Abhijit Champanerkar, Ilya Kofman, Jessica S. Purcell","submitted_at":"2014-11-28T15:47:54Z","abstract_excerpt":"The ratio of volume to crossing number of a hyperbolic knot is known to be bounded above by the volume of a regular ideal octahedron, and a similar bound is conjectured for the knot determinant per crossing. We investigate a natural question motivated by these bounds: For which knots are these ratios nearly maximal? We show that many families of alternating knots and links simultaneously maximize both ratios."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7915","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":""},"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":"1411.7915","created_at":"2026-05-18T00:00:41.680443+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.7915v4","created_at":"2026-05-18T00:00:41.680443+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7915","created_at":"2026-05-18T00:00:41.680443+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PCBVUPPRLOB","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PCBVUPPRLOBDMZL","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PCBVUPP","created_at":"2026-05-18T12:28:16.859392+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/6PCBVUPPRLOBDMZL7MONS6FVRN","json":"https://pith.science/pith/6PCBVUPPRLOBDMZL7MONS6FVRN.json","graph_json":"https://pith.science/api/pith-number/6PCBVUPPRLOBDMZL7MONS6FVRN/graph.json","events_json":"https://pith.science/api/pith-number/6PCBVUPPRLOBDMZL7MONS6FVRN/events.json","paper":"https://pith.science/paper/6PCBVUPP"},"agent_actions":{"view_html":"https://pith.science/pith/6PCBVUPPRLOBDMZL7MONS6FVRN","download_json":"https://pith.science/pith/6PCBVUPPRLOBDMZL7MONS6FVRN.json","view_paper":"https://pith.science/paper/6PCBVUPP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.7915&json=true","fetch_graph":"https://pith.science/api/pith-number/6PCBVUPPRLOBDMZL7MONS6FVRN/graph.json","fetch_events":"https://pith.science/api/pith-number/6PCBVUPPRLOBDMZL7MONS6FVRN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PCBVUPPRLOBDMZL7MONS6FVRN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PCBVUPPRLOBDMZL7MONS6FVRN/action/storage_attestation","attest_author":"https://pith.science/pith/6PCBVUPPRLOBDMZL7MONS6FVRN/action/author_attestation","sign_citation":"https://pith.science/pith/6PCBVUPPRLOBDMZL7MONS6FVRN/action/citation_signature","submit_replication":"https://pith.science/pith/6PCBVUPPRLOBDMZL7MONS6FVRN/action/replication_record"}},"created_at":"2026-05-18T00:00:41.680443+00:00","updated_at":"2026-05-18T00:00:41.680443+00:00"}