{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MRO6APRDOLK4ZOL4ZMLNP6KNLW","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":"2630f29e50b8961e2cd68efd8145b245619c80acf1d6c4f12a1394281f6a209a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-10T17:24:49Z","title_canon_sha256":"2031fe8c1e77e7059c925a1939a666c57b9918c2af6a37f29437888c99fdfed7"},"schema_version":"1.0","source":{"id":"1411.2509","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2509","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2509v2","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2509","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"MRO6APRDOLK4","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MRO6APRDOLK4ZOL4","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MRO6APRD","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:3521426c68f39bf513f30fa64aec6f27cfe48d9771c3d1134982f453a15c581e","target":"graph","created_at":"2026-05-18T00:00:46Z","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":"The main result is a short effective proof of Tao Li's theorem that a closed non Haken hyperbolic 3-manifold N has at most finitely many irreducible Heegaard splittings.","authors_text":"David Gabai, Tobias Holck Colding","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-10T17:24:49Z","title":"Effective Finiteness of irreducible Heegaard splittings of non Haken 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2509","kind":"arxiv","version":2},"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:e46d429689340cf0f8a416fd765f68351a01407b28afd76c486376c0e8dfd72e","target":"record","created_at":"2026-05-18T00:00:46Z","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":"2630f29e50b8961e2cd68efd8145b245619c80acf1d6c4f12a1394281f6a209a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-10T17:24:49Z","title_canon_sha256":"2031fe8c1e77e7059c925a1939a666c57b9918c2af6a37f29437888c99fdfed7"},"schema_version":"1.0","source":{"id":"1411.2509","kind":"arxiv","version":2}},"canonical_sha256":"645de03e2372d5ccb97ccb16d7f94d5d991f5df390a6cd05411a1ffff622a7eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"645de03e2372d5ccb97ccb16d7f94d5d991f5df390a6cd05411a1ffff622a7eb","first_computed_at":"2026-05-18T00:00:46.097154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:46.097154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PsCO/W02Jgv6/96iWtf3YrW1kaH/3VnY3s9BkIuStB8XYowbLFXICZSbxyBa09nDpkVOWDkktNi3M/JODgaRDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:46.097659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2509","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e46d429689340cf0f8a416fd765f68351a01407b28afd76c486376c0e8dfd72e","sha256:3521426c68f39bf513f30fa64aec6f27cfe48d9771c3d1134982f453a15c581e"],"state_sha256":"2422110b134b7822921252f381dde5e7482963c72a64c48169972760ebede668"}