{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:WBEMKDUULWU3P55BRI5OXZAHZZ","short_pith_number":"pith:WBEMKDUU","schema_version":"1.0","canonical_sha256":"b048c50e945da9b7f7a18a3aebe407ce6f5a6113b21c9d55c2c347ccecb12824","source":{"kind":"arxiv","id":"0905.3788","version":2},"attestation_state":"computed","paper":{"title":"An Elementary Proof by the Heegaard Splittings of the 3-Dimentional Poincare Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Shunji Horiguchi","submitted_at":"2009-05-23T04:41:07Z","abstract_excerpt":"v1: In this paper, we will give an elementary proof by the Heegaard splittings of the 3-dimentional Poincare conjecture in point of view of PL topology. This paper is of the same theory in [4](1983) excluding the last three lines of the proof of the main theorem. v2: This paper gives the basic result of [1](1997), i.e., a handle sliding and a band move of Heegaard diagrams correspond to a replacement and a substitution in relations of the fundamental groups derived from Heegaard diagrams, respectively (Theorem 12). Corollary 13 is a new addition for the homotopy 3-sphere."},"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":"0905.3788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2009-05-23T04:41:07Z","cross_cats_sorted":[],"title_canon_sha256":"e83813b69fd4195cc40676b6039d782eae1ed173f616494f96237060adb56413","abstract_canon_sha256":"2cfec10dca7e3b278747c444e18ed3a1b6dfd2e6ff84a6b7caa7ef8d412c32a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:05.229032Z","signature_b64":"KT+VhdTbGV7GPo7NMrXYqEsOipWuIlnfFpmkzbe7saxa4ENKwP1pif4HBpkmnWqemw/GK+sVfInsEl7wgwpUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b048c50e945da9b7f7a18a3aebe407ce6f5a6113b21c9d55c2c347ccecb12824","last_reissued_at":"2026-05-18T03:38:05.228430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:05.228430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Elementary Proof by the Heegaard Splittings of the 3-Dimentional Poincare Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Shunji Horiguchi","submitted_at":"2009-05-23T04:41:07Z","abstract_excerpt":"v1: In this paper, we will give an elementary proof by the Heegaard splittings of the 3-dimentional Poincare conjecture in point of view of PL topology. This paper is of the same theory in [4](1983) excluding the last three lines of the proof of the main theorem. v2: This paper gives the basic result of [1](1997), i.e., a handle sliding and a band move of Heegaard diagrams correspond to a replacement and a substitution in relations of the fundamental groups derived from Heegaard diagrams, respectively (Theorem 12). Corollary 13 is a new addition for the homotopy 3-sphere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3788","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":"0905.3788","created_at":"2026-05-18T03:38:05.228528+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.3788v2","created_at":"2026-05-18T03:38:05.228528+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3788","created_at":"2026-05-18T03:38:05.228528+00:00"},{"alias_kind":"pith_short_12","alias_value":"WBEMKDUULWU3","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"WBEMKDUULWU3P55B","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"WBEMKDUU","created_at":"2026-05-18T12:26:02.257875+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/WBEMKDUULWU3P55BRI5OXZAHZZ","json":"https://pith.science/pith/WBEMKDUULWU3P55BRI5OXZAHZZ.json","graph_json":"https://pith.science/api/pith-number/WBEMKDUULWU3P55BRI5OXZAHZZ/graph.json","events_json":"https://pith.science/api/pith-number/WBEMKDUULWU3P55BRI5OXZAHZZ/events.json","paper":"https://pith.science/paper/WBEMKDUU"},"agent_actions":{"view_html":"https://pith.science/pith/WBEMKDUULWU3P55BRI5OXZAHZZ","download_json":"https://pith.science/pith/WBEMKDUULWU3P55BRI5OXZAHZZ.json","view_paper":"https://pith.science/paper/WBEMKDUU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.3788&json=true","fetch_graph":"https://pith.science/api/pith-number/WBEMKDUULWU3P55BRI5OXZAHZZ/graph.json","fetch_events":"https://pith.science/api/pith-number/WBEMKDUULWU3P55BRI5OXZAHZZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WBEMKDUULWU3P55BRI5OXZAHZZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WBEMKDUULWU3P55BRI5OXZAHZZ/action/storage_attestation","attest_author":"https://pith.science/pith/WBEMKDUULWU3P55BRI5OXZAHZZ/action/author_attestation","sign_citation":"https://pith.science/pith/WBEMKDUULWU3P55BRI5OXZAHZZ/action/citation_signature","submit_replication":"https://pith.science/pith/WBEMKDUULWU3P55BRI5OXZAHZZ/action/replication_record"}},"created_at":"2026-05-18T03:38:05.228528+00:00","updated_at":"2026-05-18T03:38:05.228528+00:00"}