{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CDWXA53BX73CIVKHIKJEXOUURB","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":"37b45b9ea2a0ca6bb87ee77647a1d2d726df34c50d1523b834738fada85eb10a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-11-24T15:50:03Z","title_canon_sha256":"2f32deb59d5aa9867ad56d865fd32b7744616e286ccc2d32273000c4ce686524"},"schema_version":"1.0","source":{"id":"0811.3899","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.3899","created_at":"2026-05-18T04:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"0811.3899v2","created_at":"2026-05-18T04:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.3899","created_at":"2026-05-18T04:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"CDWXA53BX73C","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CDWXA53BX73CIVKH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CDWXA53B","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:ce767fd09d2690fba512f102941b11d5f25734bd257b12e3a02aa87ab9665fe3","target":"graph","created_at":"2026-05-18T04:12:43Z","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"},"paper":{"abstract_excerpt":"We prove that some Riemannian manifolds with boundary under an explicit integral pinching are spherical space forms. Precisely, we show that 3-dimensional Riemannian manifolds with totally geodesic boundary, positive scalar curvature and an explicit integral pinching between the $L^2$-norm of their scalar curvature and the $L^2$-norm of their Ricci tensor are spherical space forms with totally geodesic boundary. Moreover, we prove also that 4-dimensional Riemannian manifolds with umbilic boundary, positive Yamabe invariant and an explicit integral pinching between the total integral of their $","authors_text":"Cheikh Birahim Ndiaye, Giovanni Catino","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-11-24T15:50:03Z","title":"Integral pinching results for manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3899","kind":"arxiv","version":2},"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":"sha256:531a68a214dc18c0b9e15ddc2d6612403ed2bfdd22735506a1ad7e5711686e81","target":"record","created_at":"2026-05-18T04:12:43Z","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":"37b45b9ea2a0ca6bb87ee77647a1d2d726df34c50d1523b834738fada85eb10a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-11-24T15:50:03Z","title_canon_sha256":"2f32deb59d5aa9867ad56d865fd32b7744616e286ccc2d32273000c4ce686524"},"schema_version":"1.0","source":{"id":"0811.3899","kind":"arxiv","version":2}},"canonical_sha256":"10ed707761bff624554742924bba94887dc9267269015e2b3aaa095c70413193","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10ed707761bff624554742924bba94887dc9267269015e2b3aaa095c70413193","first_computed_at":"2026-05-18T04:12:43.223566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:43.223566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2NKNyMzHQkW8aS1LATW3ZLw2mnWeMS8ZKd6g6eEq79ZtYUOSBmmLsorO7AbitOtruT7vga+O3ygPeC/p2WgzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:43.224289Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.3899","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:531a68a214dc18c0b9e15ddc2d6612403ed2bfdd22735506a1ad7e5711686e81","sha256:ce767fd09d2690fba512f102941b11d5f25734bd257b12e3a02aa87ab9665fe3"],"state_sha256":"71a3284c2b8aabe8d2fb8fdfa7d522df1ec134b628725cccc0af0b8e91321112"}