{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:N723KQFDRFROSFX6GFUSIH76HZ","short_pith_number":"pith:N723KQFD","schema_version":"1.0","canonical_sha256":"6ff5b540a38962e916fe3169241ffe3e733837b0e5603dbcc8fb9e09a98158b6","source":{"kind":"arxiv","id":"2201.05595","version":3},"attestation_state":"computed","paper":{"title":"Geometry of three-dimensional manifolds with positive scalar curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jiaping Wang, Ovidiu Munteanu","submitted_at":"2022-01-14T18:35:23Z","abstract_excerpt":"The purpose of this paper is to derive volume and other geometric information for three-dimensional complete manifolds with positive scalar curvature. In the case that the Ricci curvature is nonnegative, it is shown that the volume of the manifold must be of linear growth when the scalar curvature is bounded from below by a positive constant. This answers a question of Gromov in the affirmative for dimension three. Volume growth estimates are also obtained for the case when scalar curvature decays to zero. In fact, results of similar nature are established for the more general case that the Ri"},"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":"2201.05595","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-01-14T18:35:23Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"7435658b333d3c47b80562979dd8bb9228f6ca3cd3569d19142e1884acf28563","abstract_canon_sha256":"c6569b5816b1f15757ff324f61330fa9097c3417149893ba1a259b4a8a67a6ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:54.757464Z","signature_b64":"RK3X2ppJjsASIMwgyQFDDO04O0EU6y4nEaqbmzcOaohrA1D/Az3u+G1O2Xgb9tUJjkS7CU3o4D4mwDBknsjzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ff5b540a38962e916fe3169241ffe3e733837b0e5603dbcc8fb9e09a98158b6","last_reissued_at":"2026-07-05T08:26:54.756872Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:54.756872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry of three-dimensional manifolds with positive scalar curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jiaping Wang, Ovidiu Munteanu","submitted_at":"2022-01-14T18:35:23Z","abstract_excerpt":"The purpose of this paper is to derive volume and other geometric information for three-dimensional complete manifolds with positive scalar curvature. In the case that the Ricci curvature is nonnegative, it is shown that the volume of the manifold must be of linear growth when the scalar curvature is bounded from below by a positive constant. This answers a question of Gromov in the affirmative for dimension three. Volume growth estimates are also obtained for the case when scalar curvature decays to zero. In fact, results of similar nature are established for the more general case that the Ri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.05595","kind":"arxiv","version":3},"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/2201.05595/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":"2201.05595","created_at":"2026-07-05T08:26:54.756952+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.05595v3","created_at":"2026-07-05T08:26:54.756952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.05595","created_at":"2026-07-05T08:26:54.756952+00:00"},{"alias_kind":"pith_short_12","alias_value":"N723KQFDRFRO","created_at":"2026-07-05T08:26:54.756952+00:00"},{"alias_kind":"pith_short_16","alias_value":"N723KQFDRFROSFX6","created_at":"2026-07-05T08:26:54.756952+00:00"},{"alias_kind":"pith_short_8","alias_value":"N723KQFD","created_at":"2026-07-05T08:26:54.756952+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.01368","citing_title":"Cohn--Vossen-Type Inequalities for Three-Manifolds and Locally Conformally Flat Manifolds","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2409.00583","citing_title":"Notes on scalar curvature lower bounds of steady gradient Ricci solitons","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ","json":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ.json","graph_json":"https://pith.science/api/pith-number/N723KQFDRFROSFX6GFUSIH76HZ/graph.json","events_json":"https://pith.science/api/pith-number/N723KQFDRFROSFX6GFUSIH76HZ/events.json","paper":"https://pith.science/paper/N723KQFD"},"agent_actions":{"view_html":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ","download_json":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ.json","view_paper":"https://pith.science/paper/N723KQFD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.05595&json=true","fetch_graph":"https://pith.science/api/pith-number/N723KQFDRFROSFX6GFUSIH76HZ/graph.json","fetch_events":"https://pith.science/api/pith-number/N723KQFDRFROSFX6GFUSIH76HZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ/action/storage_attestation","attest_author":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ/action/author_attestation","sign_citation":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ/action/citation_signature","submit_replication":"https://pith.science/pith/N723KQFDRFROSFX6GFUSIH76HZ/action/replication_record"}},"created_at":"2026-07-05T08:26:54.756952+00:00","updated_at":"2026-07-05T08:26:54.756952+00:00"}