{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ORLRY4MBODJGBPCYGYKYKNZDA4","short_pith_number":"pith:ORLRY4MB","schema_version":"1.0","canonical_sha256":"74571c718170d260bc583615853723072ee7c59f8299a9c8ed901adf7595d937","source":{"kind":"arxiv","id":"1706.01037","version":2},"attestation_state":"computed","paper":{"title":"Local min-max surfaces and strongly irreducible minimal Heegaard splittings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antoine Song","submitted_at":"2017-06-04T06:55:48Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.01037","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-04T06:55:48Z","cross_cats_sorted":[],"title_canon_sha256":"afe5636b289eaf95bae3eefb2d4dd7a3f9eb4c6a30f87e179a951b9f42c6bea7","abstract_canon_sha256":"5a2d73dd92c1e8dca5871b2009f3ad540e5c06fa6a0bc8bc7cdd52d115ae5572"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:20:30.196966Z","signature_b64":"DTfp1/Xhav20Z0B7pqqbicodUoq4lVOWn8eaYEezfIN6tfyBUTDA0D28XdKGz1tEbK5F8sEYQMIeG/347kguBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74571c718170d260bc583615853723072ee7c59f8299a9c8ed901adf7595d937","last_reissued_at":"2026-07-05T00:20:30.196404Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:20:30.196404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local min-max surfaces and strongly irreducible minimal Heegaard splittings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antoine Song","submitted_at":"2017-06-04T06:55:48Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01037","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1706.01037/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.01037","created_at":"2026-07-05T00:20:30.196465+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.01037v2","created_at":"2026-07-05T00:20:30.196465+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01037","created_at":"2026-07-05T00:20:30.196465+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORLRY4MBODJG","created_at":"2026-07-05T00:20:30.196465+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORLRY4MBODJGBPCY","created_at":"2026-07-05T00:20:30.196465+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORLRY4MB","created_at":"2026-07-05T00:20:30.196465+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.12428","citing_title":"A min-max gap characterization of minimal foliations on the torus","ref_index":44,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12428","citing_title":"A min-max gap characterization of minimal foliations on the torus","ref_index":44,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4","json":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4.json","graph_json":"https://pith.science/api/pith-number/ORLRY4MBODJGBPCYGYKYKNZDA4/graph.json","events_json":"https://pith.science/api/pith-number/ORLRY4MBODJGBPCYGYKYKNZDA4/events.json","paper":"https://pith.science/paper/ORLRY4MB"},"agent_actions":{"view_html":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4","download_json":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4.json","view_paper":"https://pith.science/paper/ORLRY4MB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.01037&json=true","fetch_graph":"https://pith.science/api/pith-number/ORLRY4MBODJGBPCYGYKYKNZDA4/graph.json","fetch_events":"https://pith.science/api/pith-number/ORLRY4MBODJGBPCYGYKYKNZDA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4/action/storage_attestation","attest_author":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4/action/author_attestation","sign_citation":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4/action/citation_signature","submit_replication":"https://pith.science/pith/ORLRY4MBODJGBPCYGYKYKNZDA4/action/replication_record"}},"created_at":"2026-07-05T00:20:30.196465+00:00","updated_at":"2026-07-05T00:20:30.196465+00:00"}