{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:K7X7NVOGIB3ELS4AM67RGYCPHM","short_pith_number":"pith:K7X7NVOG","schema_version":"1.0","canonical_sha256":"57eff6d5c6407645cb8067bf13604f3b13a8372f23055604e40fec40db0ff9a2","source":{"kind":"arxiv","id":"gr-qc/0312047","version":2},"attestation_state":"computed","paper":{"title":"The Penrose Inequality","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Hubert L. Bray, Piotr T. Chrusciel","submitted_at":"2003-12-08T23:08:19Z","abstract_excerpt":"In 1973, R. Penrose presented an argument that the total mass of a space-time which contains black holes with event horizons of total area $A$ should be at least $\\sqrt{A/16\\pi}$. An important special case of this physical statement translates into a very beautiful mathematical inequality in Riemannian geometry known as the Riemannian Penrose inequality. This inequality was first established by G. Huisken and T. Ilmanen in 1997 for a single black hole and then by one of the authors (H.B.) in 1999 for any number of black holes. The two approaches use two different geometric flow techniques and "},"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":"gr-qc/0312047","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2003-12-08T23:08:19Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"22ee432fb4683fcf1de0a5e595de312d29c8c7111130f720c85165b8d21ab6e1","abstract_canon_sha256":"e4788fe6b3461439d0f5a7e04d90702d1f055ecafde245d3d967ebf05a36732c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:25:43.725004Z","signature_b64":"FcJwdRDh5Inf6mpYs+b0fUVsmKfDE42grlC9iWgdCqSJQ6QefBY5kj9Nd1GR/Nx+dWOulmnMGHFhwkbuIYFEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57eff6d5c6407645cb8067bf13604f3b13a8372f23055604e40fec40db0ff9a2","last_reissued_at":"2026-07-04T14:25:43.724568Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:25:43.724568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Penrose Inequality","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Hubert L. Bray, Piotr T. Chrusciel","submitted_at":"2003-12-08T23:08:19Z","abstract_excerpt":"In 1973, R. Penrose presented an argument that the total mass of a space-time which contains black holes with event horizons of total area $A$ should be at least $\\sqrt{A/16\\pi}$. An important special case of this physical statement translates into a very beautiful mathematical inequality in Riemannian geometry known as the Riemannian Penrose inequality. This inequality was first established by G. Huisken and T. Ilmanen in 1997 for a single black hole and then by one of the authors (H.B.) in 1999 for any number of black holes. The two approaches use two different geometric flow techniques and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0312047","kind":"arxiv","version":2},"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/gr-qc/0312047/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":"gr-qc/0312047","created_at":"2026-07-04T14:25:43.724636+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0312047v2","created_at":"2026-07-04T14:25:43.724636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0312047","created_at":"2026-07-04T14:25:43.724636+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7X7NVOGIB3E","created_at":"2026-07-04T14:25:43.724636+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7X7NVOGIB3ELS4A","created_at":"2026-07-04T14:25:43.724636+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7X7NVOG","created_at":"2026-07-04T14:25:43.724636+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.17812","citing_title":"Black Hole Entropy Bounded by the Specific Heat","ref_index":33,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM","json":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM.json","graph_json":"https://pith.science/api/pith-number/K7X7NVOGIB3ELS4AM67RGYCPHM/graph.json","events_json":"https://pith.science/api/pith-number/K7X7NVOGIB3ELS4AM67RGYCPHM/events.json","paper":"https://pith.science/paper/K7X7NVOG"},"agent_actions":{"view_html":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM","download_json":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM.json","view_paper":"https://pith.science/paper/K7X7NVOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0312047&json=true","fetch_graph":"https://pith.science/api/pith-number/K7X7NVOGIB3ELS4AM67RGYCPHM/graph.json","fetch_events":"https://pith.science/api/pith-number/K7X7NVOGIB3ELS4AM67RGYCPHM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM/action/storage_attestation","attest_author":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM/action/author_attestation","sign_citation":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM/action/citation_signature","submit_replication":"https://pith.science/pith/K7X7NVOGIB3ELS4AM67RGYCPHM/action/replication_record"}},"created_at":"2026-07-04T14:25:43.724636+00:00","updated_at":"2026-07-04T14:25:43.724636+00:00"}