{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:35VDL2ZIUNISAXA2VHCL6R36LL","short_pith_number":"pith:35VDL2ZI","canonical_record":{"source":{"id":"0912.0830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-12-04T12:06:50Z","cross_cats_sorted":[],"title_canon_sha256":"6cb83dce80abcc4ef379db79a6550ab60e9e0473901694c41259bbace989fe9f","abstract_canon_sha256":"bc61bb4aecf1d18d3cb88f0f68581261382d260d5618eb6abfd2103d0cd26378"},"schema_version":"1.0"},"canonical_sha256":"df6a35eb28a351205c1aa9c4bf477e5af3d610eb8eae10b0dc48763d9e7a5619","source":{"kind":"arxiv","id":"0912.0830","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0830","created_at":"2026-05-18T04:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0830v3","created_at":"2026-05-18T04:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0830","created_at":"2026-05-18T04:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"35VDL2ZIUNIS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"35VDL2ZIUNISAXA2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"35VDL2ZI","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:35VDL2ZIUNISAXA2VHCL6R36LL","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-12-04T12:06:50Z","cross_cats_sorted":[],"title_canon_sha256":"6cb83dce80abcc4ef379db79a6550ab60e9e0473901694c41259bbace989fe9f","abstract_canon_sha256":"bc61bb4aecf1d18d3cb88f0f68581261382d260d5618eb6abfd2103d0cd26378"},"schema_version":"1.0"},"canonical_sha256":"df6a35eb28a351205c1aa9c4bf477e5af3d610eb8eae10b0dc48763d9e7a5619","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:15.468564Z","signature_b64":"W2HBnzurCqshEejW87zj+iahbapd7EbqZB6q48HJmLBpGV+VNapzjnhSC5Gr/QzEV77hB1KyYLLfbYhitqApBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df6a35eb28a351205c1aa9c4bf477e5af3d610eb8eae10b0dc48763d9e7a5619","last_reissued_at":"2026-05-18T04:04:15.467797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:15.467797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0830","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:04:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cn26H8ZjXCU9xLHponyC/vEOMftJVcKYR8kns5HyoDmUWQ1tbJxGe3v8E9CLlIpAXJkbxIhkDWOfFlJ/Rem+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:14:38.053787Z"},"content_sha256":"c3843595cca602d6c224e39929d39e67c3b8124cc6e005dbac3db59b1ef8c26c","schema_version":"1.0","event_id":"sha256:c3843595cca602d6c224e39929d39e67c3b8124cc6e005dbac3db59b1ef8c26c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:35VDL2ZIUNISAXA2VHCL6R36LL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial Heegaard Floer homology and nice Heegaard diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andras I. Stipsicz, Peter S. Ozsvath, Zoltan Szabo","submitted_at":"2009-12-04T12:06:50Z","abstract_excerpt":"We consider a stabilized version of hat Heegaard Floer homology of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for Y, and give a combinatorial proof of its invariance properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0830","kind":"arxiv","version":3},"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":"2026-05-18T04:04:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKFFvepOMpDPGtb9RUaYKw3KHVJMWEveG2Mv4r+LbGLXRRbGlMq25jp1iaMU5xAxnQqOGSNVC+jdQn7dEy6XAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:14:38.054370Z"},"content_sha256":"aeb1abb8fb3f13039e6c37e82576af68694114e20a6360156c3554bf5f03382a","schema_version":"1.0","event_id":"sha256:aeb1abb8fb3f13039e6c37e82576af68694114e20a6360156c3554bf5f03382a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/35VDL2ZIUNISAXA2VHCL6R36LL/bundle.json","state_url":"https://pith.science/pith/35VDL2ZIUNISAXA2VHCL6R36LL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/35VDL2ZIUNISAXA2VHCL6R36LL/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":"2026-05-30T23:14:38Z","links":{"resolver":"https://pith.science/pith/35VDL2ZIUNISAXA2VHCL6R36LL","bundle":"https://pith.science/pith/35VDL2ZIUNISAXA2VHCL6R36LL/bundle.json","state":"https://pith.science/pith/35VDL2ZIUNISAXA2VHCL6R36LL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/35VDL2ZIUNISAXA2VHCL6R36LL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:35VDL2ZIUNISAXA2VHCL6R36LL","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":"bc61bb4aecf1d18d3cb88f0f68581261382d260d5618eb6abfd2103d0cd26378","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-12-04T12:06:50Z","title_canon_sha256":"6cb83dce80abcc4ef379db79a6550ab60e9e0473901694c41259bbace989fe9f"},"schema_version":"1.0","source":{"id":"0912.0830","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0830","created_at":"2026-05-18T04:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0830v3","created_at":"2026-05-18T04:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0830","created_at":"2026-05-18T04:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"35VDL2ZIUNIS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"35VDL2ZIUNISAXA2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"35VDL2ZI","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:aeb1abb8fb3f13039e6c37e82576af68694114e20a6360156c3554bf5f03382a","target":"graph","created_at":"2026-05-18T04:04:15Z","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 consider a stabilized version of hat Heegaard Floer homology of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for Y, and give a combinatorial proof of its invariance properties.","authors_text":"Andras I. Stipsicz, Peter S. Ozsvath, Zoltan Szabo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-12-04T12:06:50Z","title":"Combinatorial Heegaard Floer homology and nice Heegaard diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0830","kind":"arxiv","version":3},"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:c3843595cca602d6c224e39929d39e67c3b8124cc6e005dbac3db59b1ef8c26c","target":"record","created_at":"2026-05-18T04:04:15Z","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":"bc61bb4aecf1d18d3cb88f0f68581261382d260d5618eb6abfd2103d0cd26378","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-12-04T12:06:50Z","title_canon_sha256":"6cb83dce80abcc4ef379db79a6550ab60e9e0473901694c41259bbace989fe9f"},"schema_version":"1.0","source":{"id":"0912.0830","kind":"arxiv","version":3}},"canonical_sha256":"df6a35eb28a351205c1aa9c4bf477e5af3d610eb8eae10b0dc48763d9e7a5619","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df6a35eb28a351205c1aa9c4bf477e5af3d610eb8eae10b0dc48763d9e7a5619","first_computed_at":"2026-05-18T04:04:15.467797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:15.467797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2HBnzurCqshEejW87zj+iahbapd7EbqZB6q48HJmLBpGV+VNapzjnhSC5Gr/QzEV77hB1KyYLLfbYhitqApBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:15.468564Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0830","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3843595cca602d6c224e39929d39e67c3b8124cc6e005dbac3db59b1ef8c26c","sha256:aeb1abb8fb3f13039e6c37e82576af68694114e20a6360156c3554bf5f03382a"],"state_sha256":"7542935847f0cd50485a2f2d3c8f47992fdc2e0cbe3d16eaf298c9ec01c7fab5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PX/jOXoLgt6QDBPk5i+EXCvvLBwmmIrGUbXufWErXZV8Oi5310Gw7SArXepRkH2qsBJneIHJ91JvprYTQctjBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:14:38.058086Z","bundle_sha256":"5b6da06e451cc0d362052cf1d0cc2b32a3f07d74ea56541bfb56794aca7b7700"}}