{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZK4LN4HAB6WCWRHILW7UDGPPBF","short_pith_number":"pith:ZK4LN4HA","schema_version":"1.0","canonical_sha256":"cab8b6f0e00fac2b44e85dbf4199ef09490aefa51c470aece7327e55290bc9dd","source":{"kind":"arxiv","id":"1709.03804","version":2},"attestation_state":"computed","paper":{"title":"Elimination of definite fold II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Osamu Saeki","submitted_at":"2017-09-12T12:26:02Z","abstract_excerpt":"In this paper, we first give a new simple proof to the elimination theorem of definite fold by homotopy for generic smooth maps of manifolds of dimension strictly greater than $2$ into the $2$--sphere or into the real projective plane. Our new proof has the advantage that it is not only constructive, but is also algorithmic: the procedures enable us to construct various explicit examples. We also study simple stable maps of $3$--manifolds into the $2$--sphere without definite fold. Furthermore, we prove the non-existence of singular Legendre fibrations on $3$--manifolds, answering negatively t"},"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":"1709.03804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-09-12T12:26:02Z","cross_cats_sorted":[],"title_canon_sha256":"96fee7c3c948ae5ceeac6eb99c4e04f2103d42cc50ae59c3a706bb832c53364c","abstract_canon_sha256":"0cc0c5b9901992230d895f79d42651c32da739adabc1e20bd4db01f30b91d1e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:41.857099Z","signature_b64":"pmgAbAf+Sw7cWNG3Ic2lQJlJnoTjkZ9nAo7Iezc+HbvS7XqftJ6iiTqQB31JG2iedg07GN8epgBOVvOJX7GqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cab8b6f0e00fac2b44e85dbf4199ef09490aefa51c470aece7327e55290bc9dd","last_reissued_at":"2026-05-18T00:19:41.856404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:41.856404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elimination of definite fold II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Osamu Saeki","submitted_at":"2017-09-12T12:26:02Z","abstract_excerpt":"In this paper, we first give a new simple proof to the elimination theorem of definite fold by homotopy for generic smooth maps of manifolds of dimension strictly greater than $2$ into the $2$--sphere or into the real projective plane. Our new proof has the advantage that it is not only constructive, but is also algorithmic: the procedures enable us to construct various explicit examples. We also study simple stable maps of $3$--manifolds into the $2$--sphere without definite fold. Furthermore, we prove the non-existence of singular Legendre fibrations on $3$--manifolds, answering negatively t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03804","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":""},"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":"1709.03804","created_at":"2026-05-18T00:19:41.856521+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.03804v2","created_at":"2026-05-18T00:19:41.856521+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03804","created_at":"2026-05-18T00:19:41.856521+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZK4LN4HAB6WC","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZK4LN4HAB6WCWRHI","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZK4LN4HA","created_at":"2026-05-18T12:31:59.375834+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF","json":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF.json","graph_json":"https://pith.science/api/pith-number/ZK4LN4HAB6WCWRHILW7UDGPPBF/graph.json","events_json":"https://pith.science/api/pith-number/ZK4LN4HAB6WCWRHILW7UDGPPBF/events.json","paper":"https://pith.science/paper/ZK4LN4HA"},"agent_actions":{"view_html":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF","download_json":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF.json","view_paper":"https://pith.science/paper/ZK4LN4HA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.03804&json=true","fetch_graph":"https://pith.science/api/pith-number/ZK4LN4HAB6WCWRHILW7UDGPPBF/graph.json","fetch_events":"https://pith.science/api/pith-number/ZK4LN4HAB6WCWRHILW7UDGPPBF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF/action/storage_attestation","attest_author":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF/action/author_attestation","sign_citation":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF/action/citation_signature","submit_replication":"https://pith.science/pith/ZK4LN4HAB6WCWRHILW7UDGPPBF/action/replication_record"}},"created_at":"2026-05-18T00:19:41.856521+00:00","updated_at":"2026-05-18T00:19:41.856521+00:00"}