{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ORLRY4MBODJGBPCYGYKYKNZDA4","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":"5a2d73dd92c1e8dca5871b2009f3ad540e5c06fa6a0bc8bc7cdd52d115ae5572","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-04T06:55:48Z","title_canon_sha256":"afe5636b289eaf95bae3eefb2d4dd7a3f9eb4c6a30f87e179a951b9f42c6bea7"},"schema_version":"1.0","source":{"id":"1706.01037","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01037","created_at":"2026-07-05T00:20:30Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01037v2","created_at":"2026-07-05T00:20:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01037","created_at":"2026-07-05T00:20:30Z"},{"alias_kind":"pith_short_12","alias_value":"ORLRY4MBODJG","created_at":"2026-07-05T00:20:30Z"},{"alias_kind":"pith_short_16","alias_value":"ORLRY4MBODJGBPCY","created_at":"2026-07-05T00:20:30Z"},{"alias_kind":"pith_short_8","alias_value":"ORLRY4MB","created_at":"2026-07-05T00:20:30Z"}],"graph_snapshots":[{"event_id":"sha256:7b7a09f0ca79d8d958e1b1142dff87555d79a8af9eaa7cc425a800770e10aafa","target":"graph","created_at":"2026-07-05T00:20:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1706.01037/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $(M,g)$ be a closed oriented Riemannian $3$-manifold and suppose that there is a strongly irreducible Heegaard splitting $H$. We prove that $H$ is either isotopic to a minimal surface of index at most one or isotopic to the stable oriented double cover of a non-orientable minimal surface with a vertical handle attached. In particular, this proves a result conjectured by Rubinstein. Some consequences include the existence in any $\\mathbb{R}P^3$ of either a minimal torus or a minimal projective plane with stable universal cover. In the case of positive scalar curvature, it is shown for spher","authors_text":"Antoine Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-04T06:55:48Z","title":"Local min-max surfaces and strongly irreducible minimal Heegaard splittings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01037","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":"sha256:2599a9afe07f2ec22e14c40ced988753e31e5e622eaa3f5b9d965ef097fa1a9d","target":"record","created_at":"2026-07-05T00:20:30Z","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":"5a2d73dd92c1e8dca5871b2009f3ad540e5c06fa6a0bc8bc7cdd52d115ae5572","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-04T06:55:48Z","title_canon_sha256":"afe5636b289eaf95bae3eefb2d4dd7a3f9eb4c6a30f87e179a951b9f42c6bea7"},"schema_version":"1.0","source":{"id":"1706.01037","kind":"arxiv","version":2}},"canonical_sha256":"74571c718170d260bc583615853723072ee7c59f8299a9c8ed901adf7595d937","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74571c718170d260bc583615853723072ee7c59f8299a9c8ed901adf7595d937","first_computed_at":"2026-07-05T00:20:30.196404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:20:30.196404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DTfp1/Xhav20Z0B7pqqbicodUoq4lVOWn8eaYEezfIN6tfyBUTDA0D28XdKGz1tEbK5F8sEYQMIeG/347kguBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:20:30.196966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.01037","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2599a9afe07f2ec22e14c40ced988753e31e5e622eaa3f5b9d965ef097fa1a9d","sha256:7b7a09f0ca79d8d958e1b1142dff87555d79a8af9eaa7cc425a800770e10aafa"],"state_sha256":"94f7cf59a84aa08394879beeae294eea436ea0cd9414974589581a8171d925b7"}