{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:J52CLFRJOGR7OBKY4Y4DUSR5IV","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":"10ffaa9780952f472b3a494e028348352b18d0978f5065dd7b10fa2599ef55f5","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-05T13:21:55Z","title_canon_sha256":"5887a7dd53e299d493f0ea230357d9d3d280c2642ec8edb4feca6a8e6a22a6f5"},"schema_version":"1.0","source":{"id":"1205.1132","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1132","created_at":"2026-07-05T03:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1132v3","created_at":"2026-07-05T03:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1132","created_at":"2026-07-05T03:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"J52CLFRJOGR7","created_at":"2026-07-05T03:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"J52CLFRJOGR7OBKY","created_at":"2026-07-05T03:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"J52CLFRJ","created_at":"2026-07-05T03:01:31Z"}],"graph_snapshots":[{"event_id":"sha256:e6637af07dab62e797b6d30c5f3aaab13d436f34da81b4e662e29dbaad64014c","target":"graph","created_at":"2026-07-05T03:01:31Z","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/1205.1132/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note we prove a global rigidity result for asymptotically flat, scalar flat Euclidean hypersurfaces with a minimal horizon lying in a hyperplane, under a natural ellipticity condition. As a consequence we obtain, in the context of the Riemannian Penrose conjecture, a local rigidity result for the family of exterior Schwarzschild solutions (viewed as graphs in Euclidean space).","authors_text":"Frederico Gir\\~ao, Levi Lopes de Lima","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-05T13:21:55Z","title":"A rigidity result for the graph case of the Penrose inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1132","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:d197036ddb0154f0810468f60b4c551ebc22ff8793e5582df1c6a807be4f36fc","target":"record","created_at":"2026-07-05T03:01:31Z","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":"10ffaa9780952f472b3a494e028348352b18d0978f5065dd7b10fa2599ef55f5","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-05T13:21:55Z","title_canon_sha256":"5887a7dd53e299d493f0ea230357d9d3d280c2642ec8edb4feca6a8e6a22a6f5"},"schema_version":"1.0","source":{"id":"1205.1132","kind":"arxiv","version":3}},"canonical_sha256":"4f7425962971a3f70558e6383a4a3d4571403bd991de57182899e406eb269c12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f7425962971a3f70558e6383a4a3d4571403bd991de57182899e406eb269c12","first_computed_at":"2026-07-05T03:01:31.288935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:01:31.288935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zHzB8lotBdJCUCDOsqzF3EvMMPs07zEMG7nKOFi0tTOikL6w7xrBgkix38MAp9o7146MWHThf112AVSfsMBKBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:01:31.289410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1132","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d197036ddb0154f0810468f60b4c551ebc22ff8793e5582df1c6a807be4f36fc","sha256:e6637af07dab62e797b6d30c5f3aaab13d436f34da81b4e662e29dbaad64014c"],"state_sha256":"f82ef6d91444427124aa925f51372e3e8dc4619bfcc7cf7aa0a1f593dd7667db"}