{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:KRLCFZZOEUUCIP7XT22CYA3YWD","short_pith_number":"pith:KRLCFZZO","schema_version":"1.0","canonical_sha256":"545622e72e2528243ff79eb42c0378b0c7341d6a16b921a8a4fe8e3261245a53","source":{"kind":"arxiv","id":"0804.0112","version":1},"attestation_state":"computed","paper":{"title":"Commensurability classes of (-2,3,n) pretzel knot complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Melissa L. Macasieb, Thomas W. Mattman","submitted_at":"2008-04-01T18:25:40Z","abstract_excerpt":"Let K be a hyperbolic (-2,3,n) pretzel knot and M = S^3 K its complement. For these knots, we verify a conjecture of Reid and Walsh: there are at most three knot complements in the commensurability class of M. Indeed, if n \\neq 7, we show that M is the unique knot complement in its class. We include examples to illustrate how our methods apply to a broad class of Montesinos knots."},"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":"0804.0112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-04-01T18:25:40Z","cross_cats_sorted":[],"title_canon_sha256":"a7b62c09ac7f8136e49b571af11ab93e3453260dff6668c8b2af1527aa185cac","abstract_canon_sha256":"4a347d06eebe051cdf82ffee937084b73ee3811b4260e0e99404ebf032cfda95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.705060Z","signature_b64":"d4kG4KwKC0vUwvjtiijfI2vrhQfMQY40MvdjF3GSoCjNZ7wMbXt0ieaIiWcx5q0eMDGY27gAhCg5acLaLSGSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"545622e72e2528243ff79eb42c0378b0c7341d6a16b921a8a4fe8e3261245a53","last_reissued_at":"2026-05-18T02:41:51.704426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.704426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commensurability classes of (-2,3,n) pretzel knot complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Melissa L. Macasieb, Thomas W. Mattman","submitted_at":"2008-04-01T18:25:40Z","abstract_excerpt":"Let K be a hyperbolic (-2,3,n) pretzel knot and M = S^3 K its complement. For these knots, we verify a conjecture of Reid and Walsh: there are at most three knot complements in the commensurability class of M. Indeed, if n \\neq 7, we show that M is the unique knot complement in its class. We include examples to illustrate how our methods apply to a broad class of Montesinos knots."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0112","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":"0804.0112","created_at":"2026-05-18T02:41:51.704515+00:00"},{"alias_kind":"arxiv_version","alias_value":"0804.0112v1","created_at":"2026-05-18T02:41:51.704515+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.0112","created_at":"2026-05-18T02:41:51.704515+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRLCFZZOEUUC","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRLCFZZOEUUCIP7X","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRLCFZZO","created_at":"2026-05-18T12:25:57.157939+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/KRLCFZZOEUUCIP7XT22CYA3YWD","json":"https://pith.science/pith/KRLCFZZOEUUCIP7XT22CYA3YWD.json","graph_json":"https://pith.science/api/pith-number/KRLCFZZOEUUCIP7XT22CYA3YWD/graph.json","events_json":"https://pith.science/api/pith-number/KRLCFZZOEUUCIP7XT22CYA3YWD/events.json","paper":"https://pith.science/paper/KRLCFZZO"},"agent_actions":{"view_html":"https://pith.science/pith/KRLCFZZOEUUCIP7XT22CYA3YWD","download_json":"https://pith.science/pith/KRLCFZZOEUUCIP7XT22CYA3YWD.json","view_paper":"https://pith.science/paper/KRLCFZZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0804.0112&json=true","fetch_graph":"https://pith.science/api/pith-number/KRLCFZZOEUUCIP7XT22CYA3YWD/graph.json","fetch_events":"https://pith.science/api/pith-number/KRLCFZZOEUUCIP7XT22CYA3YWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRLCFZZOEUUCIP7XT22CYA3YWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRLCFZZOEUUCIP7XT22CYA3YWD/action/storage_attestation","attest_author":"https://pith.science/pith/KRLCFZZOEUUCIP7XT22CYA3YWD/action/author_attestation","sign_citation":"https://pith.science/pith/KRLCFZZOEUUCIP7XT22CYA3YWD/action/citation_signature","submit_replication":"https://pith.science/pith/KRLCFZZOEUUCIP7XT22CYA3YWD/action/replication_record"}},"created_at":"2026-05-18T02:41:51.704515+00:00","updated_at":"2026-05-18T02:41:51.704515+00:00"}