{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:WKJSFXSBCRPDLFPEENI4OATZCR","short_pith_number":"pith:WKJSFXSB","schema_version":"1.0","canonical_sha256":"b29322de41145e3595e42351c70279144eae8612c44378e56bb6797ac5f15c8e","source":{"kind":"arxiv","id":"0811.2254","version":2},"attestation_state":"computed","paper":{"title":"On the tunnel number and the Morse-Novikov number of knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"A. Pajitnov","submitted_at":"2008-11-14T02:09:01Z","abstract_excerpt":"We prove that the Morse-Novikov number of a link L in a 3-sphere is less than or equal to twice the tunnel number of L."},"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":"0811.2254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-11-14T02:09:01Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6fccde96798b6581a588829e72a578fef4e3f1e9d685b572638ccf036e5085bf","abstract_canon_sha256":"5031074fe0f5f8084b8091ffde4768fa66b7786db5c49b67ca66dc1044281151"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:31.072728Z","signature_b64":"N4ORRuE8h/JdtrbG7aYVa8RgHX1DbVQiN0GdMmaCeExEJQBMP6WzNMND39m/p6vELBZP8j3aXbuS1AFDnMujDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b29322de41145e3595e42351c70279144eae8612c44378e56bb6797ac5f15c8e","last_reissued_at":"2026-05-18T01:22:31.072190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:31.072190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the tunnel number and the Morse-Novikov number of knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"A. Pajitnov","submitted_at":"2008-11-14T02:09:01Z","abstract_excerpt":"We prove that the Morse-Novikov number of a link L in a 3-sphere is less than or equal to twice the tunnel number of L."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.2254","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":"0811.2254","created_at":"2026-05-18T01:22:31.072282+00:00"},{"alias_kind":"arxiv_version","alias_value":"0811.2254v2","created_at":"2026-05-18T01:22:31.072282+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.2254","created_at":"2026-05-18T01:22:31.072282+00:00"},{"alias_kind":"pith_short_12","alias_value":"WKJSFXSBCRPD","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"WKJSFXSBCRPDLFPE","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"WKJSFXSB","created_at":"2026-05-18T12:25:58.018023+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/WKJSFXSBCRPDLFPEENI4OATZCR","json":"https://pith.science/pith/WKJSFXSBCRPDLFPEENI4OATZCR.json","graph_json":"https://pith.science/api/pith-number/WKJSFXSBCRPDLFPEENI4OATZCR/graph.json","events_json":"https://pith.science/api/pith-number/WKJSFXSBCRPDLFPEENI4OATZCR/events.json","paper":"https://pith.science/paper/WKJSFXSB"},"agent_actions":{"view_html":"https://pith.science/pith/WKJSFXSBCRPDLFPEENI4OATZCR","download_json":"https://pith.science/pith/WKJSFXSBCRPDLFPEENI4OATZCR.json","view_paper":"https://pith.science/paper/WKJSFXSB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0811.2254&json=true","fetch_graph":"https://pith.science/api/pith-number/WKJSFXSBCRPDLFPEENI4OATZCR/graph.json","fetch_events":"https://pith.science/api/pith-number/WKJSFXSBCRPDLFPEENI4OATZCR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WKJSFXSBCRPDLFPEENI4OATZCR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WKJSFXSBCRPDLFPEENI4OATZCR/action/storage_attestation","attest_author":"https://pith.science/pith/WKJSFXSBCRPDLFPEENI4OATZCR/action/author_attestation","sign_citation":"https://pith.science/pith/WKJSFXSBCRPDLFPEENI4OATZCR/action/citation_signature","submit_replication":"https://pith.science/pith/WKJSFXSBCRPDLFPEENI4OATZCR/action/replication_record"}},"created_at":"2026-05-18T01:22:31.072282+00:00","updated_at":"2026-05-18T01:22:31.072282+00:00"}