{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IKPBXMJHIOFOMU2PZ65IPTV3KS","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":"5aad54a6152ad58d449ea3cd3f25bbffdf3887cf4a4730eb77441f5ebb640e38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-29T20:00:04Z","title_canon_sha256":"248a3beeb5dc9838e4cce5097d3077191cd5d972dc032b844fd4ad07bb0554d2"},"schema_version":"1.0","source":{"id":"1410.8133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8133","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8133v1","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8133","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"IKPBXMJHIOFO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IKPBXMJHIOFOMU2P","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IKPBXMJH","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:fa12298680a68c3ab203831865b5f5243b3b75bb8288c0292dbb48c20b4ad6dd","target":"graph","created_at":"2026-05-18T00:42:33Z","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 show that the only closed 4-manifolds admitting genus two trisections are $S^2 \\times S^2$ and connected sums of $S^1 \\times S^3$, $\\mathbb{CP}^2$, and $\\overline{\\mathbb{CP}}^2$ with two summands. Moreover, each of these manifolds admits a unique genus two trisection up to diffeomorphism. The proof relies heavily on the combinatorics of genus two Heegaard diagrams of $S^3$. As a corollary, we classify two-component links contained in a genus two Heegaard surface for $S^3$ with a surface-sloped cosmetic Dehn surgery.","authors_text":"Alexander Zupan, Jeffrey Meier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-29T20:00:04Z","title":"Genus two trisections are standard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8133","kind":"arxiv","version":1},"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:b03d209fde1d91abf0764a33a49263ac51575286d6f1a69fc78631bd993e0c79","target":"record","created_at":"2026-05-18T00:42:33Z","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":"5aad54a6152ad58d449ea3cd3f25bbffdf3887cf4a4730eb77441f5ebb640e38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-29T20:00:04Z","title_canon_sha256":"248a3beeb5dc9838e4cce5097d3077191cd5d972dc032b844fd4ad07bb0554d2"},"schema_version":"1.0","source":{"id":"1410.8133","kind":"arxiv","version":1}},"canonical_sha256":"429e1bb127438ae6534fcfba87cebb54857101e71a6153558e4f04f5d5a400be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"429e1bb127438ae6534fcfba87cebb54857101e71a6153558e4f04f5d5a400be","first_computed_at":"2026-05-18T00:42:33.625129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:33.625129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dFpXQJX9DPdrh1BlBy8GAMUwECcCqSYbAaIV/Fk12XGAsOwjYB1kE7FpY6t65sukqOpM42T4VaGBt+GTj3kjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:33.625582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b03d209fde1d91abf0764a33a49263ac51575286d6f1a69fc78631bd993e0c79","sha256:fa12298680a68c3ab203831865b5f5243b3b75bb8288c0292dbb48c20b4ad6dd"],"state_sha256":"c04aa0395d5ca412f3c9b3809cef33bc0fd5a553d695dd6f79debb39781037d3"}