{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:67BQIYVQCZS2UI234T3CRNMCFJ","short_pith_number":"pith:67BQIYVQ","schema_version":"1.0","canonical_sha256":"f7c30462b01665aa235be4f628b5822a50e40487c532e16c81ba98d7c1a12cbb","source":{"kind":"arxiv","id":"1904.01439","version":2},"attestation_state":"computed","paper":{"title":"Trisections of 5-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Maggie Miller, Peter Lambert-Cole","submitted_at":"2019-04-02T14:06:24Z","abstract_excerpt":"Gay and Kirby introduced the notion of a trisection of a smooth 4-manifold, which is a decomposition of the 4-manifold into three elementary pieces. Rubinstein and Tillmann later extended this idea to construct multisections of piecewise-linear (PL) manifolds in all dimensions. Given a PL manifold $Y$ of dimension $n$, this is a decomposition of $Y$ into $\\lfloor \\frac{n}{2} \\rfloor + 1$ PL submanifolds. We show that every smooth, oriented, compact 5-manifold admits a smooth trisection compatible with any desired trisection of its boundary."},"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":"1904.01439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-02T14:06:24Z","cross_cats_sorted":[],"title_canon_sha256":"a85c2aed2c998b641aa9d69221ff5ab91a1c181f6d596f4acccf79a161ea6408","abstract_canon_sha256":"ec7a7ef5de715ed3d62fb471f4b09410532494dedc4ed69e07613e56f4186f57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:24.345009Z","signature_b64":"SVp6DgOmgR1cJMdwOeG0py3f4b55nenPUGCfLSDDgDDaTik6FCh90Db3N//YZqdIlioyweBfWImvgYuiIfylBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7c30462b01665aa235be4f628b5822a50e40487c532e16c81ba98d7c1a12cbb","last_reissued_at":"2026-05-17T23:49:24.344425Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:24.344425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trisections of 5-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Maggie Miller, Peter Lambert-Cole","submitted_at":"2019-04-02T14:06:24Z","abstract_excerpt":"Gay and Kirby introduced the notion of a trisection of a smooth 4-manifold, which is a decomposition of the 4-manifold into three elementary pieces. Rubinstein and Tillmann later extended this idea to construct multisections of piecewise-linear (PL) manifolds in all dimensions. Given a PL manifold $Y$ of dimension $n$, this is a decomposition of $Y$ into $\\lfloor \\frac{n}{2} \\rfloor + 1$ PL submanifolds. We show that every smooth, oriented, compact 5-manifold admits a smooth trisection compatible with any desired trisection of its boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01439","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":"1904.01439","created_at":"2026-05-17T23:49:24.344499+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.01439v2","created_at":"2026-05-17T23:49:24.344499+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01439","created_at":"2026-05-17T23:49:24.344499+00:00"},{"alias_kind":"pith_short_12","alias_value":"67BQIYVQCZS2","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"67BQIYVQCZS2UI23","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"67BQIYVQ","created_at":"2026-05-18T12:33:10.108867+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/67BQIYVQCZS2UI234T3CRNMCFJ","json":"https://pith.science/pith/67BQIYVQCZS2UI234T3CRNMCFJ.json","graph_json":"https://pith.science/api/pith-number/67BQIYVQCZS2UI234T3CRNMCFJ/graph.json","events_json":"https://pith.science/api/pith-number/67BQIYVQCZS2UI234T3CRNMCFJ/events.json","paper":"https://pith.science/paper/67BQIYVQ"},"agent_actions":{"view_html":"https://pith.science/pith/67BQIYVQCZS2UI234T3CRNMCFJ","download_json":"https://pith.science/pith/67BQIYVQCZS2UI234T3CRNMCFJ.json","view_paper":"https://pith.science/paper/67BQIYVQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.01439&json=true","fetch_graph":"https://pith.science/api/pith-number/67BQIYVQCZS2UI234T3CRNMCFJ/graph.json","fetch_events":"https://pith.science/api/pith-number/67BQIYVQCZS2UI234T3CRNMCFJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/67BQIYVQCZS2UI234T3CRNMCFJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/67BQIYVQCZS2UI234T3CRNMCFJ/action/storage_attestation","attest_author":"https://pith.science/pith/67BQIYVQCZS2UI234T3CRNMCFJ/action/author_attestation","sign_citation":"https://pith.science/pith/67BQIYVQCZS2UI234T3CRNMCFJ/action/citation_signature","submit_replication":"https://pith.science/pith/67BQIYVQCZS2UI234T3CRNMCFJ/action/replication_record"}},"created_at":"2026-05-17T23:49:24.344499+00:00","updated_at":"2026-05-17T23:49:24.344499+00:00"}