{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:7PCUPTDGY5KKJ4ZA4OICGOOICL","short_pith_number":"pith:7PCUPTDG","canonical_record":{"source":{"id":"2212.14383","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-12-29T17:25:15Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"79aeeaafa38fd80c9ff2d1d3091a974b15510b8941215743281487bf0532e433","abstract_canon_sha256":"39ffdcdb68e9e5142ff4462322d72cf7518a0334188fc208509e9d8e11ffcc85"},"schema_version":"1.0"},"canonical_sha256":"fbc547cc66c754a4f320e3902339c812d8260012ea279046822d01f08de81be3","source":{"kind":"arxiv","id":"2212.14383","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.14383","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"arxiv_version","alias_value":"2212.14383v3","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.14383","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_12","alias_value":"7PCUPTDGY5KK","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7PCUPTDGY5KKJ4ZA","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7PCUPTDG","created_at":"2026-07-05T11:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:7PCUPTDGY5KKJ4ZA4OICGOOICL","target":"record","payload":{"canonical_record":{"source":{"id":"2212.14383","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-12-29T17:25:15Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"79aeeaafa38fd80c9ff2d1d3091a974b15510b8941215743281487bf0532e433","abstract_canon_sha256":"39ffdcdb68e9e5142ff4462322d72cf7518a0334188fc208509e9d8e11ffcc85"},"schema_version":"1.0"},"canonical_sha256":"fbc547cc66c754a4f320e3902339c812d8260012ea279046822d01f08de81be3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:58.388788Z","signature_b64":"OU0dFcopIDiciR9bx4bNoeRJXaSX5076V2E4cgFF+Uf1aMS25HqYPqlwM7MPrDz65u1H8kmmiRH9giWBkL+/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbc547cc66c754a4f320e3902339c812d8260012ea279046822d01f08de81be3","last_reissued_at":"2026-07-05T11:25:58.388348Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:58.388348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.14383","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:25:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGr236RxlnBj7qV6DMcAbnhxseNlwJQFmm6Qnr/T1GGE/VD0pgegfDlX5M3ONY4mrtTnUr7K7wxJZbYDn7ZvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:15:25.895063Z"},"content_sha256":"3bf430338dfaca399a71fa141ac06d0ee75ca09c59f4e7ca1ea55a12408f768e","schema_version":"1.0","event_id":"sha256:3bf430338dfaca399a71fa141ac06d0ee75ca09c59f4e7ca1ea55a12408f768e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:7PCUPTDGY5KKJ4ZA4OICGOOICL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology of $3$-manifolds with uniformly positive scalar curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Jian Wang (AMSS)","submitted_at":"2022-12-29T17:25:15Z","abstract_excerpt":"In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is homeomorphic to an (possibly) infinite connected sum of spherical $3$-manifolds and some copies of $\\mathbb{S}^1\\times \\mathbb{S}^2$. Further, we study an oriented $3$-manifold with mean convex boundary and with uniformly positive scalar curvature. If the boundary is a disjoint union of closed surfaces, then the manifold is an (possibly) infinite conned sum of spher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.14383","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/2212.14383/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:25:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9h1DpuPqgfbXNd9sPIe3sz+kHe32SxJFOKl+cWR2jguO7fe6kKxerxzwBOkgFZTSTCJ0EaNQlQXn9zpDOIaNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:15:25.895587Z"},"content_sha256":"8c194214e196e37ec118d5296ec35b6066d4772d2fecd6498bb3180782e6a469","schema_version":"1.0","event_id":"sha256:8c194214e196e37ec118d5296ec35b6066d4772d2fecd6498bb3180782e6a469"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7PCUPTDGY5KKJ4ZA4OICGOOICL/bundle.json","state_url":"https://pith.science/pith/7PCUPTDGY5KKJ4ZA4OICGOOICL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7PCUPTDGY5KKJ4ZA4OICGOOICL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T00:15:25Z","links":{"resolver":"https://pith.science/pith/7PCUPTDGY5KKJ4ZA4OICGOOICL","bundle":"https://pith.science/pith/7PCUPTDGY5KKJ4ZA4OICGOOICL/bundle.json","state":"https://pith.science/pith/7PCUPTDGY5KKJ4ZA4OICGOOICL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7PCUPTDGY5KKJ4ZA4OICGOOICL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7PCUPTDGY5KKJ4ZA4OICGOOICL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"39ffdcdb68e9e5142ff4462322d72cf7518a0334188fc208509e9d8e11ffcc85","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-12-29T17:25:15Z","title_canon_sha256":"79aeeaafa38fd80c9ff2d1d3091a974b15510b8941215743281487bf0532e433"},"schema_version":"1.0","source":{"id":"2212.14383","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.14383","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"arxiv_version","alias_value":"2212.14383v3","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.14383","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_12","alias_value":"7PCUPTDGY5KK","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7PCUPTDGY5KKJ4ZA","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7PCUPTDG","created_at":"2026-07-05T11:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:8c194214e196e37ec118d5296ec35b6066d4772d2fecd6498bb3180782e6a469","target":"graph","created_at":"2026-07-05T11:25:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.14383/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is homeomorphic to an (possibly) infinite connected sum of spherical $3$-manifolds and some copies of $\\mathbb{S}^1\\times \\mathbb{S}^2$. Further, we study an oriented $3$-manifold with mean convex boundary and with uniformly positive scalar curvature. If the boundary is a disjoint union of closed surfaces, then the manifold is an (possibly) infinite conned sum of spher","authors_text":"Jian Wang (AMSS)","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-12-29T17:25:15Z","title":"Topology of $3$-manifolds with uniformly positive scalar curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.14383","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3bf430338dfaca399a71fa141ac06d0ee75ca09c59f4e7ca1ea55a12408f768e","target":"record","created_at":"2026-07-05T11:25:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"39ffdcdb68e9e5142ff4462322d72cf7518a0334188fc208509e9d8e11ffcc85","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-12-29T17:25:15Z","title_canon_sha256":"79aeeaafa38fd80c9ff2d1d3091a974b15510b8941215743281487bf0532e433"},"schema_version":"1.0","source":{"id":"2212.14383","kind":"arxiv","version":3}},"canonical_sha256":"fbc547cc66c754a4f320e3902339c812d8260012ea279046822d01f08de81be3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbc547cc66c754a4f320e3902339c812d8260012ea279046822d01f08de81be3","first_computed_at":"2026-07-05T11:25:58.388348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:25:58.388348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OU0dFcopIDiciR9bx4bNoeRJXaSX5076V2E4cgFF+Uf1aMS25HqYPqlwM7MPrDz65u1H8kmmiRH9giWBkL+/CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:25:58.388788Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.14383","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bf430338dfaca399a71fa141ac06d0ee75ca09c59f4e7ca1ea55a12408f768e","sha256:8c194214e196e37ec118d5296ec35b6066d4772d2fecd6498bb3180782e6a469"],"state_sha256":"f135f2642708c74ccb0b6e16de10865313dc501f0924bb07609a5d94dccf6a47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A6RfQQ2eewviX46Fd1sh1FONAZqlin9939c0Cwvq6Rwt+3Hc8XMeHQe3iCpJ17sEWMuD9KJCRh2QOtSzzoYjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T00:15:25.900221Z","bundle_sha256":"d5fd24d10e12538b6337d535198fe7d9cf77d2d6d845df0a183ee832772cb520"}}