{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KHK3745HPNRWKF7QDXFHPNWBTO","short_pith_number":"pith:KHK3745H","schema_version":"1.0","canonical_sha256":"51d5bff3a77b636517f01dca77b6c19bae24e49f00945444fa595d4dc95e865d","source":{"kind":"arxiv","id":"1011.6304","version":4},"attestation_state":"computed","paper":{"title":"Region crossing change is an unknotting operation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ayaka Shimizu","submitted_at":"2010-11-29T17:45:14Z","abstract_excerpt":"Region crossing change is a local transformation on a knot or link diagram. We show that a region crossing change on a knot diagram is an unknotting operation, and we define the region unknotting numbers for a knot diagram and a knot."},"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":"1011.6304","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-11-29T17:45:14Z","cross_cats_sorted":[],"title_canon_sha256":"965b30eaa3f3dcc02d685ceb969372d71a0d47f662e324f6fe54d59a134f2775","abstract_canon_sha256":"8f0cb71243edb76b08d21d2ca06b4ad5d40a0174b4a8268831e07b21bd23f02c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:07.711696Z","signature_b64":"hkaqnC292+uZxv+4Mt/c6RZEiz1D5D1Ik0ui9ILIHHXrqsoqaD7SKnZGC/5l8frI8cOXEFrn8loLEKS9zEr/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51d5bff3a77b636517f01dca77b6c19bae24e49f00945444fa595d4dc95e865d","last_reissued_at":"2026-05-18T03:02:07.710888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:07.710888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Region crossing change is an unknotting operation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ayaka Shimizu","submitted_at":"2010-11-29T17:45:14Z","abstract_excerpt":"Region crossing change is a local transformation on a knot or link diagram. We show that a region crossing change on a knot diagram is an unknotting operation, and we define the region unknotting numbers for a knot diagram and a knot."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6304","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":"1011.6304","created_at":"2026-05-18T03:02:07.711020+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.6304v4","created_at":"2026-05-18T03:02:07.711020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6304","created_at":"2026-05-18T03:02:07.711020+00:00"},{"alias_kind":"pith_short_12","alias_value":"KHK3745HPNRW","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KHK3745HPNRWKF7Q","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KHK3745H","created_at":"2026-05-18T12:26:09.077623+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/KHK3745HPNRWKF7QDXFHPNWBTO","json":"https://pith.science/pith/KHK3745HPNRWKF7QDXFHPNWBTO.json","graph_json":"https://pith.science/api/pith-number/KHK3745HPNRWKF7QDXFHPNWBTO/graph.json","events_json":"https://pith.science/api/pith-number/KHK3745HPNRWKF7QDXFHPNWBTO/events.json","paper":"https://pith.science/paper/KHK3745H"},"agent_actions":{"view_html":"https://pith.science/pith/KHK3745HPNRWKF7QDXFHPNWBTO","download_json":"https://pith.science/pith/KHK3745HPNRWKF7QDXFHPNWBTO.json","view_paper":"https://pith.science/paper/KHK3745H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.6304&json=true","fetch_graph":"https://pith.science/api/pith-number/KHK3745HPNRWKF7QDXFHPNWBTO/graph.json","fetch_events":"https://pith.science/api/pith-number/KHK3745HPNRWKF7QDXFHPNWBTO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KHK3745HPNRWKF7QDXFHPNWBTO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KHK3745HPNRWKF7QDXFHPNWBTO/action/storage_attestation","attest_author":"https://pith.science/pith/KHK3745HPNRWKF7QDXFHPNWBTO/action/author_attestation","sign_citation":"https://pith.science/pith/KHK3745HPNRWKF7QDXFHPNWBTO/action/citation_signature","submit_replication":"https://pith.science/pith/KHK3745HPNRWKF7QDXFHPNWBTO/action/replication_record"}},"created_at":"2026-05-18T03:02:07.711020+00:00","updated_at":"2026-05-18T03:02:07.711020+00:00"}