{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:P7VHVIRNFH7HTCR3XHDU7WG253","short_pith_number":"pith:P7VHVIRN","canonical_record":{"source":{"id":"1103.4805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-24T16:48:35Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"2f3e95037b0d3a7a41a27ffb69c6f96ebace02d69d18b57cfbf7ba7f3a303592","abstract_canon_sha256":"6f0d5d4d24fa333f4dcb9193681994b52b0c18666d88f5cdeec694c66f86e9d8"},"schema_version":"1.0"},"canonical_sha256":"7fea7aa22d29fe798a3bb9c74fd8daeed673f29fa714a4c5ee5fa8861bed57ef","source":{"kind":"arxiv","id":"1103.4805","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4805","created_at":"2026-05-18T04:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4805v1","created_at":"2026-05-18T04:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4805","created_at":"2026-05-18T04:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"P7VHVIRNFH7H","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P7VHVIRNFH7HTCR3","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P7VHVIRN","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:P7VHVIRNFH7HTCR3XHDU7WG253","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-24T16:48:35Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"2f3e95037b0d3a7a41a27ffb69c6f96ebace02d69d18b57cfbf7ba7f3a303592","abstract_canon_sha256":"6f0d5d4d24fa333f4dcb9193681994b52b0c18666d88f5cdeec694c66f86e9d8"},"schema_version":"1.0"},"canonical_sha256":"7fea7aa22d29fe798a3bb9c74fd8daeed673f29fa714a4c5ee5fa8861bed57ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:00.846665Z","signature_b64":"WIf/JjnWUYQkfUzlWYKfk+fDkad/jzJuD4K8QYCVMOwt4IpvJ8KMz/urvTQpf927BHuZUFrzdgbALaLo3maFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fea7aa22d29fe798a3bb9c74fd8daeed673f29fa714a4c5ee5fa8861bed57ef","last_reissued_at":"2026-05-18T04:26:00.846237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:00.846237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4805","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2s8ivtoNGPWMfn1hhCOiVEEeKBefVILha+q/N9keAxZAd6ZibhDEeUB/V9lTbNsi4uPtgRXG9UKudzPKX7TOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:33:06.500175Z"},"content_sha256":"8495b07601be5ea1cf9a2e21ddabb2f34596db81fa944320ed746203ce64b2d2","schema_version":"1.0","event_id":"sha256:8495b07601be5ea1cf9a2e21ddabb2f34596db81fa944320ed746203ce64b2d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:P7VHVIRNFH7HTCR3XHDU7WG253","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity of area-minimizing hyperbolic surfaces in three-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Ivaldo Nunes","submitted_at":"2011-03-24T16:48:35Z","abstract_excerpt":"We prove that if $M$ is a three-manifold with scalar curvature greater than or equal to -2 and $\\Sigma\\subset M$ is a two-sided compact embedded Riemann surface of genus greater than 1 which is locally area-minimizing, then the area of $\\Sigma$ is greater than or equal to $4\\pi(g(\\Sigma)-1)$, where $g(\\Sigma)$ denotes the genus of $\\Sigma$. In the equality case, we prove that the induced metric on $\\Sigma$ has constant Gauss curvature equal to -1 and locally $M$ splits along $\\Sigma$. As a corollary, we obtain a rigidity result for cylinders $(I\\times\\Sigma,dt^2+g_{\\Sigma})$, where $I=[a,b]\\su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4805","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iq3r4jEmcyO8h6lOJsXguuYhgTigOV2v08MnP7HmNO/X8cTuFU+P/TPemSi047jkRO2/Iy/0yO9grOFocAdbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:33:06.500535Z"},"content_sha256":"40dc78f57b14e628b08ca67d5d32cec07cdc1e8eed95ceb596610339604e1dd4","schema_version":"1.0","event_id":"sha256:40dc78f57b14e628b08ca67d5d32cec07cdc1e8eed95ceb596610339604e1dd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7VHVIRNFH7HTCR3XHDU7WG253/bundle.json","state_url":"https://pith.science/pith/P7VHVIRNFH7HTCR3XHDU7WG253/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7VHVIRNFH7HTCR3XHDU7WG253/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":"2026-06-26T01:33:06Z","links":{"resolver":"https://pith.science/pith/P7VHVIRNFH7HTCR3XHDU7WG253","bundle":"https://pith.science/pith/P7VHVIRNFH7HTCR3XHDU7WG253/bundle.json","state":"https://pith.science/pith/P7VHVIRNFH7HTCR3XHDU7WG253/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7VHVIRNFH7HTCR3XHDU7WG253/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:P7VHVIRNFH7HTCR3XHDU7WG253","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":"6f0d5d4d24fa333f4dcb9193681994b52b0c18666d88f5cdeec694c66f86e9d8","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-24T16:48:35Z","title_canon_sha256":"2f3e95037b0d3a7a41a27ffb69c6f96ebace02d69d18b57cfbf7ba7f3a303592"},"schema_version":"1.0","source":{"id":"1103.4805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4805","created_at":"2026-05-18T04:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4805v1","created_at":"2026-05-18T04:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4805","created_at":"2026-05-18T04:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"P7VHVIRNFH7H","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P7VHVIRNFH7HTCR3","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P7VHVIRN","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:40dc78f57b14e628b08ca67d5d32cec07cdc1e8eed95ceb596610339604e1dd4","target":"graph","created_at":"2026-05-18T04:26:00Z","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 if $M$ is a three-manifold with scalar curvature greater than or equal to -2 and $\\Sigma\\subset M$ is a two-sided compact embedded Riemann surface of genus greater than 1 which is locally area-minimizing, then the area of $\\Sigma$ is greater than or equal to $4\\pi(g(\\Sigma)-1)$, where $g(\\Sigma)$ denotes the genus of $\\Sigma$. In the equality case, we prove that the induced metric on $\\Sigma$ has constant Gauss curvature equal to -1 and locally $M$ splits along $\\Sigma$. As a corollary, we obtain a rigidity result for cylinders $(I\\times\\Sigma,dt^2+g_{\\Sigma})$, where $I=[a,b]\\su","authors_text":"Ivaldo Nunes","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-24T16:48:35Z","title":"Rigidity of area-minimizing hyperbolic surfaces in three-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4805","kind":"arxiv","version":1},"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":"sha256:8495b07601be5ea1cf9a2e21ddabb2f34596db81fa944320ed746203ce64b2d2","target":"record","created_at":"2026-05-18T04:26:00Z","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":"6f0d5d4d24fa333f4dcb9193681994b52b0c18666d88f5cdeec694c66f86e9d8","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-24T16:48:35Z","title_canon_sha256":"2f3e95037b0d3a7a41a27ffb69c6f96ebace02d69d18b57cfbf7ba7f3a303592"},"schema_version":"1.0","source":{"id":"1103.4805","kind":"arxiv","version":1}},"canonical_sha256":"7fea7aa22d29fe798a3bb9c74fd8daeed673f29fa714a4c5ee5fa8861bed57ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fea7aa22d29fe798a3bb9c74fd8daeed673f29fa714a4c5ee5fa8861bed57ef","first_computed_at":"2026-05-18T04:26:00.846237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:00.846237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WIf/JjnWUYQkfUzlWYKfk+fDkad/jzJuD4K8QYCVMOwt4IpvJ8KMz/urvTQpf927BHuZUFrzdgbALaLo3maFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:00.846665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8495b07601be5ea1cf9a2e21ddabb2f34596db81fa944320ed746203ce64b2d2","sha256:40dc78f57b14e628b08ca67d5d32cec07cdc1e8eed95ceb596610339604e1dd4"],"state_sha256":"0d28c89991c61002f6972f832d70aa9ac25e4631b7ea1262816d862c7bcfaa42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Ls08dTTP+E+XwY4o0MuSUzxbP2grsipO6o+5wFdMrbGt9kiesN9XXZtcJ36K8OFK417gSq1nSUomRzXNf+NBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:33:06.502662Z","bundle_sha256":"421371ef94e66848a38139271d7b591891b41d832c9d8869467f1f42d484b442"}}