{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:WGYHBXIREUS6NZ3C5JAWYPT3MG","short_pith_number":"pith:WGYHBXIR","canonical_record":{"source":{"id":"0903.1773","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-03-10T18:01:16Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"2e2b94449478c6d6d2d196d045595fe5c7327fb89e2389ff0b18c7b58526f00b","abstract_canon_sha256":"06cf1da21a596981be400a3f4142c91b767a2f5cbf08b40eb96d93e28a7a9b79"},"schema_version":"1.0"},"canonical_sha256":"b1b070dd112525e6e762ea416c3e7b619f85cd569429ecc6d2f2e157f3761381","source":{"kind":"arxiv","id":"0903.1773","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1773","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1773v4","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1773","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"WGYHBXIREUS6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WGYHBXIREUS6NZ3C","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WGYHBXIR","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:WGYHBXIREUS6NZ3C5JAWYPT3MG","target":"record","payload":{"canonical_record":{"source":{"id":"0903.1773","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-03-10T18:01:16Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"2e2b94449478c6d6d2d196d045595fe5c7327fb89e2389ff0b18c7b58526f00b","abstract_canon_sha256":"06cf1da21a596981be400a3f4142c91b767a2f5cbf08b40eb96d93e28a7a9b79"},"schema_version":"1.0"},"canonical_sha256":"b1b070dd112525e6e762ea416c3e7b619f85cd569429ecc6d2f2e157f3761381","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:17.060431Z","signature_b64":"PSmBWiA5LDwmacxjUuYDT+yMzJUJ6GNdtJTv8KF+TLQIzczCGriSa414VqrEu6zFFBbVwOxoyaYG+3baZjbrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1b070dd112525e6e762ea416c3e7b619f85cd569429ecc6d2f2e157f3761381","last_reissued_at":"2026-05-18T03:39:17.059869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:17.059869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.1773","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VBXTyD1+BmNNRduzYF8lisWFb8QQKQ13GC/NO+NXH7+TN+/JNSg59bUo3CZDlPYN/PLXhYcaE0KA+HZ9g5kbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:29:36.052935Z"},"content_sha256":"055ad5e5163ba0ca077f1ef64dfdc2af33d60658903af876d64f368802ed4cba","schema_version":"1.0","event_id":"sha256:055ad5e5163ba0ca077f1ef64dfdc2af33d60658903af876d64f368802ed4cba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:WGYHBXIREUS6NZ3C5JAWYPT3MG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heegaard Floer homology of broken fibrations over the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Yanki Lekili","submitted_at":"2009-03-10T18:01:16Z","abstract_excerpt":"We extend Perutz's Lagrangian matching invariants to 3-manifolds which are not necessarily fibred using the technology of holomorphic quilts. We prove an isomorphism of these invariants with Ozsvath-Szabo's Heegaard Floer invariants for certain extremal spin^c structures. As applications, we give new calculations of Heegaard Floer homology of certain classes of 3-manifolds, and a characterization of Juhasz's sutured Floer homology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1773","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kUZo2P8k80AJ2zWI5vxpjXEIOhJVXNbMSVHW2T2Z8rpWOF3ujIs04RS7l8UhJG2+Md4ZF0+DbX/zgjTiAn45BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:29:36.053281Z"},"content_sha256":"9f32df845556fa47c55a4a4c56141c5e5ea315b9843cb3b7657cb5bd339ad733","schema_version":"1.0","event_id":"sha256:9f32df845556fa47c55a4a4c56141c5e5ea315b9843cb3b7657cb5bd339ad733"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGYHBXIREUS6NZ3C5JAWYPT3MG/bundle.json","state_url":"https://pith.science/pith/WGYHBXIREUS6NZ3C5JAWYPT3MG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGYHBXIREUS6NZ3C5JAWYPT3MG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T06:29:36Z","links":{"resolver":"https://pith.science/pith/WGYHBXIREUS6NZ3C5JAWYPT3MG","bundle":"https://pith.science/pith/WGYHBXIREUS6NZ3C5JAWYPT3MG/bundle.json","state":"https://pith.science/pith/WGYHBXIREUS6NZ3C5JAWYPT3MG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGYHBXIREUS6NZ3C5JAWYPT3MG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:WGYHBXIREUS6NZ3C5JAWYPT3MG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"06cf1da21a596981be400a3f4142c91b767a2f5cbf08b40eb96d93e28a7a9b79","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-03-10T18:01:16Z","title_canon_sha256":"2e2b94449478c6d6d2d196d045595fe5c7327fb89e2389ff0b18c7b58526f00b"},"schema_version":"1.0","source":{"id":"0903.1773","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1773","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1773v4","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1773","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"WGYHBXIREUS6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WGYHBXIREUS6NZ3C","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WGYHBXIR","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:9f32df845556fa47c55a4a4c56141c5e5ea315b9843cb3b7657cb5bd339ad733","target":"graph","created_at":"2026-05-18T03:39:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We extend Perutz's Lagrangian matching invariants to 3-manifolds which are not necessarily fibred using the technology of holomorphic quilts. We prove an isomorphism of these invariants with Ozsvath-Szabo's Heegaard Floer invariants for certain extremal spin^c structures. As applications, we give new calculations of Heegaard Floer homology of certain classes of 3-manifolds, and a characterization of Juhasz's sutured Floer homology.","authors_text":"Yanki Lekili","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-03-10T18:01:16Z","title":"Heegaard Floer homology of broken fibrations over the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1773","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:055ad5e5163ba0ca077f1ef64dfdc2af33d60658903af876d64f368802ed4cba","target":"record","created_at":"2026-05-18T03:39:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"06cf1da21a596981be400a3f4142c91b767a2f5cbf08b40eb96d93e28a7a9b79","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-03-10T18:01:16Z","title_canon_sha256":"2e2b94449478c6d6d2d196d045595fe5c7327fb89e2389ff0b18c7b58526f00b"},"schema_version":"1.0","source":{"id":"0903.1773","kind":"arxiv","version":4}},"canonical_sha256":"b1b070dd112525e6e762ea416c3e7b619f85cd569429ecc6d2f2e157f3761381","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1b070dd112525e6e762ea416c3e7b619f85cd569429ecc6d2f2e157f3761381","first_computed_at":"2026-05-18T03:39:17.059869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:17.059869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PSmBWiA5LDwmacxjUuYDT+yMzJUJ6GNdtJTv8KF+TLQIzczCGriSa414VqrEu6zFFBbVwOxoyaYG+3baZjbrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:17.060431Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1773","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:055ad5e5163ba0ca077f1ef64dfdc2af33d60658903af876d64f368802ed4cba","sha256:9f32df845556fa47c55a4a4c56141c5e5ea315b9843cb3b7657cb5bd339ad733"],"state_sha256":"da9b2e5a495847dcbae18f02d0a497d0a7bf06a94558072b617ea74f21ed44ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IM1cY+NolFYWmWQONway9KKgoEqy/1Hlct/ItdMeTBDAsZ+Kj8ywySR0MhBlapNfzNcZkXsqBGvSX2zFekgtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:29:36.055685Z","bundle_sha256":"47479774101444cd03d565e0d7ebdb108f27e159fd5633e8a0518202a29aba83"}}