{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OVPX73WNFRDC6IV4NRZ2REXO2K","short_pith_number":"pith:OVPX73WN","schema_version":"1.0","canonical_sha256":"755f7feecd2c462f22bc6c73a892eed2b9eeccd9c0dacc240372669e6589f990","source":{"kind":"arxiv","id":"1208.1526","version":2},"attestation_state":"computed","paper":{"title":"The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Ko Honda, Paolo Ghiggini, Vincent Colin","submitted_at":"2012-08-07T21:20:09Z","abstract_excerpt":"Given a closed oriented 3-manifold M, we establish an isomorphism between the Heegaard Floer homology group HF^+(-M) and the embedded contact homology group ECH(M). Starting from an open book decomposition (S,h) of M, we construct a chain map \\Phi^+ from a Heegaard Floer chain complex associated to (S,h) to an embedded contact homology chain complex for a contact form supported by (S,h). The chain map \\Phi^+ commutes up to homotopy with the U-maps defined on both sides and reduces to the quasi-isomorphism \\Phi from \"The equivalence of Heegaard Floer homology and embedded contact homology I, II"},"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":"1208.1526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-08-07T21:20:09Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"a54e9466646aac394432557a8ed01188cf8be939e53ca27ddcc2970502d51aa2","abstract_canon_sha256":"8d0e696bf8159dfc226ec5f22fc8792d331f9d42d1710700f1d99f21bb2c980c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:54.136497Z","signature_b64":"pGPtxedZJcbNUdsGeCoO0G8nz6Xr/4WWzQ2bZJ/dHsJphwyLiAWnet7jKmtv0BxD4osbhyZFGmtvsUkP0DCFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"755f7feecd2c462f22bc6c73a892eed2b9eeccd9c0dacc240372669e6589f990","last_reissued_at":"2026-05-18T00:41:54.135713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:54.135713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Ko Honda, Paolo Ghiggini, Vincent Colin","submitted_at":"2012-08-07T21:20:09Z","abstract_excerpt":"Given a closed oriented 3-manifold M, we establish an isomorphism between the Heegaard Floer homology group HF^+(-M) and the embedded contact homology group ECH(M). Starting from an open book decomposition (S,h) of M, we construct a chain map \\Phi^+ from a Heegaard Floer chain complex associated to (S,h) to an embedded contact homology chain complex for a contact form supported by (S,h). The chain map \\Phi^+ commutes up to homotopy with the U-maps defined on both sides and reduces to the quasi-isomorphism \\Phi from \"The equivalence of Heegaard Floer homology and embedded contact homology I, II"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1526","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":"1208.1526","created_at":"2026-05-18T00:41:54.135855+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.1526v2","created_at":"2026-05-18T00:41:54.135855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1526","created_at":"2026-05-18T00:41:54.135855+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVPX73WNFRDC","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVPX73WNFRDC6IV4","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVPX73WN","created_at":"2026-05-18T12:27:16.716162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2008.02755","citing_title":"On contact type hypersurfaces in 4-space","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K","json":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K.json","graph_json":"https://pith.science/api/pith-number/OVPX73WNFRDC6IV4NRZ2REXO2K/graph.json","events_json":"https://pith.science/api/pith-number/OVPX73WNFRDC6IV4NRZ2REXO2K/events.json","paper":"https://pith.science/paper/OVPX73WN"},"agent_actions":{"view_html":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K","download_json":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K.json","view_paper":"https://pith.science/paper/OVPX73WN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.1526&json=true","fetch_graph":"https://pith.science/api/pith-number/OVPX73WNFRDC6IV4NRZ2REXO2K/graph.json","fetch_events":"https://pith.science/api/pith-number/OVPX73WNFRDC6IV4NRZ2REXO2K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K/action/storage_attestation","attest_author":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K/action/author_attestation","sign_citation":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K/action/citation_signature","submit_replication":"https://pith.science/pith/OVPX73WNFRDC6IV4NRZ2REXO2K/action/replication_record"}},"created_at":"2026-05-18T00:41:54.135855+00:00","updated_at":"2026-05-18T00:41:54.135855+00:00"}