{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IMDHNYPWZYG73V7ZBZQGCXAGTI","short_pith_number":"pith:IMDHNYPW","schema_version":"1.0","canonical_sha256":"430676e1f6ce0dfdd7f90e60615c069a2e691f3f421a397897251bc9b0d62a01","source":{"kind":"arxiv","id":"1001.1458","version":1},"attestation_state":"computed","paper":{"title":"Ricci flow on open 3-manifolds and positive scalar curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"G\\'erard Besson, Laurent Bessi\\`eres, Sylvain Maillot","submitted_at":"2010-01-09T22:44:24Z","abstract_excerpt":"We show that an orientable 3-dimensional manifold M admits a complete riemannian metric of bounded geometry and uniformly pos- itive scalar curvature if and only if there exists a finite collection F of spherical space-forms such that M is a (possibly infinite) connected sum where each summand is diffeomorphic to S2xS1 or to some mem- ber of F. This result generalises G. Perelman's classification theorem for compact 3-manifolds of positive scalar curvature. The main tool is a variant of Perelman's surgery construction for Ricci flow."},"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":"1001.1458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-01-09T22:44:24Z","cross_cats_sorted":[],"title_canon_sha256":"2dbf87abac1f155bb9bfef4808b867a449ec1314a0a8d712e0fe0789482d2824","abstract_canon_sha256":"4d70ec44fd4d6a62236d4cbabf31cda5f53e48ada0d885e94ac9ba11f2827b3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.641793Z","signature_b64":"MmYheTdGs66DqEjjfnAMZjqs+biT1UQPQ1rUX7fzDAKDi+WwMf1g5Y7HtFjGwcuG51Yg4veVNDopgZWEt68NDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"430676e1f6ce0dfdd7f90e60615c069a2e691f3f421a397897251bc9b0d62a01","last_reissued_at":"2026-05-18T02:38:18.641136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.641136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ricci flow on open 3-manifolds and positive scalar curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"G\\'erard Besson, Laurent Bessi\\`eres, Sylvain Maillot","submitted_at":"2010-01-09T22:44:24Z","abstract_excerpt":"We show that an orientable 3-dimensional manifold M admits a complete riemannian metric of bounded geometry and uniformly pos- itive scalar curvature if and only if there exists a finite collection F of spherical space-forms such that M is a (possibly infinite) connected sum where each summand is diffeomorphic to S2xS1 or to some mem- ber of F. This result generalises G. Perelman's classification theorem for compact 3-manifolds of positive scalar curvature. The main tool is a variant of Perelman's surgery construction for Ricci flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1458","kind":"arxiv","version":1},"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":"1001.1458","created_at":"2026-05-18T02:38:18.641241+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.1458v1","created_at":"2026-05-18T02:38:18.641241+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1458","created_at":"2026-05-18T02:38:18.641241+00:00"},{"alias_kind":"pith_short_12","alias_value":"IMDHNYPWZYG7","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IMDHNYPWZYG73V7Z","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IMDHNYPW","created_at":"2026-05-18T12:26:09.077623+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/IMDHNYPWZYG73V7ZBZQGCXAGTI","json":"https://pith.science/pith/IMDHNYPWZYG73V7ZBZQGCXAGTI.json","graph_json":"https://pith.science/api/pith-number/IMDHNYPWZYG73V7ZBZQGCXAGTI/graph.json","events_json":"https://pith.science/api/pith-number/IMDHNYPWZYG73V7ZBZQGCXAGTI/events.json","paper":"https://pith.science/paper/IMDHNYPW"},"agent_actions":{"view_html":"https://pith.science/pith/IMDHNYPWZYG73V7ZBZQGCXAGTI","download_json":"https://pith.science/pith/IMDHNYPWZYG73V7ZBZQGCXAGTI.json","view_paper":"https://pith.science/paper/IMDHNYPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.1458&json=true","fetch_graph":"https://pith.science/api/pith-number/IMDHNYPWZYG73V7ZBZQGCXAGTI/graph.json","fetch_events":"https://pith.science/api/pith-number/IMDHNYPWZYG73V7ZBZQGCXAGTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IMDHNYPWZYG73V7ZBZQGCXAGTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IMDHNYPWZYG73V7ZBZQGCXAGTI/action/storage_attestation","attest_author":"https://pith.science/pith/IMDHNYPWZYG73V7ZBZQGCXAGTI/action/author_attestation","sign_citation":"https://pith.science/pith/IMDHNYPWZYG73V7ZBZQGCXAGTI/action/citation_signature","submit_replication":"https://pith.science/pith/IMDHNYPWZYG73V7ZBZQGCXAGTI/action/replication_record"}},"created_at":"2026-05-18T02:38:18.641241+00:00","updated_at":"2026-05-18T02:38:18.641241+00:00"}