{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PMWIWP5APYVDZIDBRS6L5RM2QZ","short_pith_number":"pith:PMWIWP5A","schema_version":"1.0","canonical_sha256":"7b2c8b3fa07e2a3ca0618cbcbec59a8640ef352b5a98f4f5806793db6f8b943f","source":{"kind":"arxiv","id":"1406.3539","version":1},"attestation_state":"computed","paper":{"title":"Regular-equivalence of $2$-knot diagrams and sphere eversions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kokoro Tanaka, Masamichi Takase","submitted_at":"2014-06-13T14:02:48Z","abstract_excerpt":"For each diagram $D$ of a $2$-knot, we provide a way to construct a new diagram $D'$ of the same knot such that any sequence of Roseman moves between $D$ and $D'$ necessarily involves branch points. The proof is done by developing the observation that no sphere eversion can be lifted to an isotopy in $4$-space."},"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":"1406.3539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-13T14:02:48Z","cross_cats_sorted":[],"title_canon_sha256":"d2e3a633caf7607dff5de033558e0e209bdc8cc5f64cc838898809d486b7d020","abstract_canon_sha256":"3e56b14af2819a83874e2d99b9bec94f80b51be6b23623a1237ce70ac3dfad86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:56.242883Z","signature_b64":"urLj0d7cr+9QGqGsOT/LXLMR9iWoNB7SMTSn2+3XpkFv0ocLGQhl8SFfeuKD8vrPDjvjrpnS3i4+92k60J+5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b2c8b3fa07e2a3ca0618cbcbec59a8640ef352b5a98f4f5806793db6f8b943f","last_reissued_at":"2026-05-18T00:18:56.242406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:56.242406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regular-equivalence of $2$-knot diagrams and sphere eversions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kokoro Tanaka, Masamichi Takase","submitted_at":"2014-06-13T14:02:48Z","abstract_excerpt":"For each diagram $D$ of a $2$-knot, we provide a way to construct a new diagram $D'$ of the same knot such that any sequence of Roseman moves between $D$ and $D'$ necessarily involves branch points. The proof is done by developing the observation that no sphere eversion can be lifted to an isotopy in $4$-space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3539","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":"1406.3539","created_at":"2026-05-18T00:18:56.242480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3539v1","created_at":"2026-05-18T00:18:56.242480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3539","created_at":"2026-05-18T00:18:56.242480+00:00"},{"alias_kind":"pith_short_12","alias_value":"PMWIWP5APYVD","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PMWIWP5APYVDZIDB","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PMWIWP5A","created_at":"2026-05-18T12:28:43.426989+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/PMWIWP5APYVDZIDBRS6L5RM2QZ","json":"https://pith.science/pith/PMWIWP5APYVDZIDBRS6L5RM2QZ.json","graph_json":"https://pith.science/api/pith-number/PMWIWP5APYVDZIDBRS6L5RM2QZ/graph.json","events_json":"https://pith.science/api/pith-number/PMWIWP5APYVDZIDBRS6L5RM2QZ/events.json","paper":"https://pith.science/paper/PMWIWP5A"},"agent_actions":{"view_html":"https://pith.science/pith/PMWIWP5APYVDZIDBRS6L5RM2QZ","download_json":"https://pith.science/pith/PMWIWP5APYVDZIDBRS6L5RM2QZ.json","view_paper":"https://pith.science/paper/PMWIWP5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3539&json=true","fetch_graph":"https://pith.science/api/pith-number/PMWIWP5APYVDZIDBRS6L5RM2QZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PMWIWP5APYVDZIDBRS6L5RM2QZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PMWIWP5APYVDZIDBRS6L5RM2QZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PMWIWP5APYVDZIDBRS6L5RM2QZ/action/storage_attestation","attest_author":"https://pith.science/pith/PMWIWP5APYVDZIDBRS6L5RM2QZ/action/author_attestation","sign_citation":"https://pith.science/pith/PMWIWP5APYVDZIDBRS6L5RM2QZ/action/citation_signature","submit_replication":"https://pith.science/pith/PMWIWP5APYVDZIDBRS6L5RM2QZ/action/replication_record"}},"created_at":"2026-05-18T00:18:56.242480+00:00","updated_at":"2026-05-18T00:18:56.242480+00:00"}