{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:ZEV5VAPRCIP3PPYI4FOWNYWXP6","short_pith_number":"pith:ZEV5VAPR","canonical_record":{"source":{"id":"2303.06788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-03-13T00:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"cde6419f1f910bb84f180ac04457216c18fe6826988e7ad70f596080323fff68","abstract_canon_sha256":"09dee35d4cc1a1ed0d896f122eb2beeba6534a4e1f70d2269f230c6563a90c37"},"schema_version":"1.0"},"canonical_sha256":"c92bda81f1121fb7bf08e15d66e2d77fad1e2af503176d61e1b41010d1fcd3d2","source":{"kind":"arxiv","id":"2303.06788","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.06788","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"2303.06788v1","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.06788","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZEV5VAPRCIP3","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"pith_short_16","alias_value":"ZEV5VAPRCIP3PPYI","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"pith_short_8","alias_value":"ZEV5VAPR","created_at":"2026-07-05T05:50:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:ZEV5VAPRCIP3PPYI4FOWNYWXP6","target":"record","payload":{"canonical_record":{"source":{"id":"2303.06788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-03-13T00:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"cde6419f1f910bb84f180ac04457216c18fe6826988e7ad70f596080323fff68","abstract_canon_sha256":"09dee35d4cc1a1ed0d896f122eb2beeba6534a4e1f70d2269f230c6563a90c37"},"schema_version":"1.0"},"canonical_sha256":"c92bda81f1121fb7bf08e15d66e2d77fad1e2af503176d61e1b41010d1fcd3d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:50:23.201285Z","signature_b64":"qokXVHXKtTZUaJJhJQIx1BLXzNr3DO2URcUT7jesd3ko1/UuUgACS+kVAsMQVuQ62f9pyvaK2YyzrnFM5Cx9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c92bda81f1121fb7bf08e15d66e2d77fad1e2af503176d61e1b41010d1fcd3d2","last_reissued_at":"2026-07-05T05:50:23.200873Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:50:23.200873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.06788","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":"2026-07-05T05:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V8mFzpSykDHa2MVaUUEJSHVZabQqQayaAuaEPm3nHTO2awwG8OR0wL5wmddRX8l7nhb/UE5RGvz/8Cyh9FjzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:27:14.088950Z"},"content_sha256":"5efe80459c9784dbc9adcb30fa295b33b6c4af8f6f44665d03b44c668398a702","schema_version":"1.0","event_id":"sha256:5efe80459c9784dbc9adcb30fa295b33b6c4af8f6f44665d03b44c668398a702"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:ZEV5VAPRCIP3PPYI4FOWNYWXP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalization of the Hawking black hole area theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Eleni-Alexandra Kontou, Veronica Sacchi","submitted_at":"2023-03-13T00:24:02Z","abstract_excerpt":"Hawking's black hole area theorem was proven using the null energy condition (NEC), a pointwise condition violated by quantum fields. The violation of the NEC is usually cited as the reason that black hole evaporation is allowed in the context of semiclassical gravity. Here we provide two generalizations of the classical black hole area theorem: First, a proof of the original theorem with an averaged condition, the weakest possible energy condition to prove the theorem using focusing of null geodesics. Second, a proof of an area-type result that allows for the shrinking of the black hole horiz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.06788","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.06788/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u9B/OUKm0UzqqExuS2dSUOPycVrZ5sr1hU+Y9UBY9HaQVpmLaeJ+g6IVWye+d8nIZ70VYhhOA45K4BU8obyiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:27:14.089452Z"},"content_sha256":"6562f747364d39bb976af83bd0a657e301aed910d99560d1af8ac0d5964451c4","schema_version":"1.0","event_id":"sha256:6562f747364d39bb976af83bd0a657e301aed910d99560d1af8ac0d5964451c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZEV5VAPRCIP3PPYI4FOWNYWXP6/bundle.json","state_url":"https://pith.science/pith/ZEV5VAPRCIP3PPYI4FOWNYWXP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZEV5VAPRCIP3PPYI4FOWNYWXP6/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":"2026-08-06T11:27:14Z","links":{"resolver":"https://pith.science/pith/ZEV5VAPRCIP3PPYI4FOWNYWXP6","bundle":"https://pith.science/pith/ZEV5VAPRCIP3PPYI4FOWNYWXP6/bundle.json","state":"https://pith.science/pith/ZEV5VAPRCIP3PPYI4FOWNYWXP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZEV5VAPRCIP3PPYI4FOWNYWXP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZEV5VAPRCIP3PPYI4FOWNYWXP6","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":"09dee35d4cc1a1ed0d896f122eb2beeba6534a4e1f70d2269f230c6563a90c37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-03-13T00:24:02Z","title_canon_sha256":"cde6419f1f910bb84f180ac04457216c18fe6826988e7ad70f596080323fff68"},"schema_version":"1.0","source":{"id":"2303.06788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.06788","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"2303.06788v1","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.06788","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZEV5VAPRCIP3","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"pith_short_16","alias_value":"ZEV5VAPRCIP3PPYI","created_at":"2026-07-05T05:50:23Z"},{"alias_kind":"pith_short_8","alias_value":"ZEV5VAPR","created_at":"2026-07-05T05:50:23Z"}],"graph_snapshots":[{"event_id":"sha256:6562f747364d39bb976af83bd0a657e301aed910d99560d1af8ac0d5964451c4","target":"graph","created_at":"2026-07-05T05:50:23Z","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/2303.06788/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hawking's black hole area theorem was proven using the null energy condition (NEC), a pointwise condition violated by quantum fields. The violation of the NEC is usually cited as the reason that black hole evaporation is allowed in the context of semiclassical gravity. Here we provide two generalizations of the classical black hole area theorem: First, a proof of the original theorem with an averaged condition, the weakest possible energy condition to prove the theorem using focusing of null geodesics. Second, a proof of an area-type result that allows for the shrinking of the black hole horiz","authors_text":"Eleni-Alexandra Kontou, Veronica Sacchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-03-13T00:24:02Z","title":"A generalization of the Hawking black hole area theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.06788","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":"sha256:5efe80459c9784dbc9adcb30fa295b33b6c4af8f6f44665d03b44c668398a702","target":"record","created_at":"2026-07-05T05:50:23Z","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":"09dee35d4cc1a1ed0d896f122eb2beeba6534a4e1f70d2269f230c6563a90c37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-03-13T00:24:02Z","title_canon_sha256":"cde6419f1f910bb84f180ac04457216c18fe6826988e7ad70f596080323fff68"},"schema_version":"1.0","source":{"id":"2303.06788","kind":"arxiv","version":1}},"canonical_sha256":"c92bda81f1121fb7bf08e15d66e2d77fad1e2af503176d61e1b41010d1fcd3d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c92bda81f1121fb7bf08e15d66e2d77fad1e2af503176d61e1b41010d1fcd3d2","first_computed_at":"2026-07-05T05:50:23.200873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:50:23.200873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qokXVHXKtTZUaJJhJQIx1BLXzNr3DO2URcUT7jesd3ko1/UuUgACS+kVAsMQVuQ62f9pyvaK2YyzrnFM5Cx9AA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:50:23.201285Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.06788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5efe80459c9784dbc9adcb30fa295b33b6c4af8f6f44665d03b44c668398a702","sha256:6562f747364d39bb976af83bd0a657e301aed910d99560d1af8ac0d5964451c4"],"state_sha256":"344826c0c0c687fcf13f0e62f06e9daea8a82ef291d27ace8bac6c21a9083d34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"koTAhkcSCN0Vglo8RrlSyF//24l6g9z987LjV+DycR9b1b8zeWbNM9X1YxNExb5uD6yCuDK0fG18fC233e8aCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T11:27:14.092754Z","bundle_sha256":"4de22b916fb882cc6c5d010fd672a535537cafb799951a191cbc377c468bcccd"}}