{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:Y4LTCTFITDF2DD7I5B42VYSKYB","short_pith_number":"pith:Y4LTCTFI","schema_version":"1.0","canonical_sha256":"c717314ca898cba18fe8e879aae24ac0476b2ee83baf1c038e220da9090f4f44","source":{"kind":"arxiv","id":"2403.14422","version":2},"attestation_state":"computed","paper":{"title":"Uniqueness of static vacuum asymptotically flat black holes and equipotential photon surfaces in $n+1$ dimensions \\`a la Robinson","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Albachiara Cogo, Benedito Leandro, Carla Cederbaum, Jo\\~ao Paulo dos Santos","submitted_at":"2024-03-21T14:19:06Z","abstract_excerpt":"In this paper, we combine and generalize to higher dimensions the approaches to proving the uniqueness of connected (3+1)-dimensional static vacuum asymptotically flat black hole spacetimes by M\\\"uller zum Hagen--Robinson--Seifert and by Robinson. Applying these techniques, we prove and/or reprove geometric inequalities for connected (n + 1)-dimensional static vacuum asymptotically flat spacetimes with either black hole or equipotential photon surface or specifically photon sphere inner boundary. In particular, assuming a natural upper bound on the total scalar curvature of the boundary, we re"},"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":"2403.14422","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-21T14:19:06Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"7c348a5ece8f48349e43f3a10a404965d534d91e3e9df8abeba61ab978c4eaba","abstract_canon_sha256":"cb00c48b9df6629be14b891917356223ef67bc33e0641647ab97ec6606286287"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:43:06.273696Z","signature_b64":"Vf9OvjbNKgWBB6uFvtTrgWHEQrqI6STEiiLLaJNaNEqojphXX3gp1co13rNq19e8roO9lILMlNLPtnBDUt45DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c717314ca898cba18fe8e879aae24ac0476b2ee83baf1c038e220da9090f4f44","last_reissued_at":"2026-07-05T09:43:06.273116Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:43:06.273116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of static vacuum asymptotically flat black holes and equipotential photon surfaces in $n+1$ dimensions \\`a la Robinson","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Albachiara Cogo, Benedito Leandro, Carla Cederbaum, Jo\\~ao Paulo dos Santos","submitted_at":"2024-03-21T14:19:06Z","abstract_excerpt":"In this paper, we combine and generalize to higher dimensions the approaches to proving the uniqueness of connected (3+1)-dimensional static vacuum asymptotically flat black hole spacetimes by M\\\"uller zum Hagen--Robinson--Seifert and by Robinson. Applying these techniques, we prove and/or reprove geometric inequalities for connected (n + 1)-dimensional static vacuum asymptotically flat spacetimes with either black hole or equipotential photon surface or specifically photon sphere inner boundary. In particular, assuming a natural upper bound on the total scalar curvature of the boundary, we re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.14422","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/2403.14422/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":"2403.14422","created_at":"2026-07-05T09:43:06.273178+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.14422v2","created_at":"2026-07-05T09:43:06.273178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.14422","created_at":"2026-07-05T09:43:06.273178+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y4LTCTFITDF2","created_at":"2026-07-05T09:43:06.273178+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y4LTCTFITDF2DD7I","created_at":"2026-07-05T09:43:06.273178+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y4LTCTFI","created_at":"2026-07-05T09:43:06.273178+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.05980","citing_title":"Charged parallel spinors and applications to mass--charge inequalities","ref_index":72,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB","json":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB.json","graph_json":"https://pith.science/api/pith-number/Y4LTCTFITDF2DD7I5B42VYSKYB/graph.json","events_json":"https://pith.science/api/pith-number/Y4LTCTFITDF2DD7I5B42VYSKYB/events.json","paper":"https://pith.science/paper/Y4LTCTFI"},"agent_actions":{"view_html":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB","download_json":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB.json","view_paper":"https://pith.science/paper/Y4LTCTFI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.14422&json=true","fetch_graph":"https://pith.science/api/pith-number/Y4LTCTFITDF2DD7I5B42VYSKYB/graph.json","fetch_events":"https://pith.science/api/pith-number/Y4LTCTFITDF2DD7I5B42VYSKYB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB/action/storage_attestation","attest_author":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB/action/author_attestation","sign_citation":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB/action/citation_signature","submit_replication":"https://pith.science/pith/Y4LTCTFITDF2DD7I5B42VYSKYB/action/replication_record"}},"created_at":"2026-07-05T09:43:06.273178+00:00","updated_at":"2026-07-05T09:43:06.273178+00:00"}