{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HT4RXBFMNPXRZ73HGEDMF24KC5","short_pith_number":"pith:HT4RXBFM","canonical_record":{"source":{"id":"1211.3494","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-11-15T05:16:08Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0c19e51ab57c9f230d1888547172852c2319d42e9cc4d3928fdcab3044d5b8a8","abstract_canon_sha256":"b70f77aa70bd8f889c62275197af5fb1fd3c7b92938c668f0d2946b8efae4a63"},"schema_version":"1.0"},"canonical_sha256":"3cf91b84ac6bef1cff673106c2eb8a1761aa89005496a883b9e80d84b97ebb48","source":{"kind":"arxiv","id":"1211.3494","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3494","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3494v4","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3494","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"HT4RXBFMNPXR","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HT4RXBFMNPXRZ73H","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HT4RXBFM","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HT4RXBFMNPXRZ73HGEDMF24KC5","target":"record","payload":{"canonical_record":{"source":{"id":"1211.3494","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-11-15T05:16:08Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0c19e51ab57c9f230d1888547172852c2319d42e9cc4d3928fdcab3044d5b8a8","abstract_canon_sha256":"b70f77aa70bd8f889c62275197af5fb1fd3c7b92938c668f0d2946b8efae4a63"},"schema_version":"1.0"},"canonical_sha256":"3cf91b84ac6bef1cff673106c2eb8a1761aa89005496a883b9e80d84b97ebb48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:47.254214Z","signature_b64":"pZEwXe2R3oqzEatgUWPfSffKQNH2EcP42V4lxYYYqCRhmbWl2i1WWEhu+KgbuqeA5e6j2zD0GO3oJzDwWiCQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cf91b84ac6bef1cff673106c2eb8a1761aa89005496a883b9e80d84b97ebb48","last_reissued_at":"2026-05-18T00:55:47.253728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:47.253728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.3494","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GJCAeN+q9SpvSiIoou5zGamNBnbQI8IFqh5IMPd4JESlbzZ0N3EtJUkvJLztVZdE5BTYaN8WgEzkklXVYgSaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:57:41.751014Z"},"content_sha256":"fe94377d60af4a023e332167d055584acd384e93759bb89c256b35c7540e1965","schema_version":"1.0","event_id":"sha256:fe94377d60af4a023e332167d055584acd384e93759bb89c256b35c7540e1965"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HT4RXBFMNPXRZ73HGEDMF24KC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Aron C. Wall","submitted_at":"2012-11-15T05:16:08Z","abstract_excerpt":"The covariant holographic entropy conjecture of AdS/CFT relates the entropy of a boundary region R to the area of an extremal surface in the bulk spacetime. This extremal surface can be obtained by a maximin construction, allowing many new results to be proven. On manifolds obeying the null curvature condition, these extremal surfaces: i) always lie outside the causal wedge of R, ii) have less area than the bifurcation surface of the causal wedge, iii) move away from the boundary as R grows, and iv) obey strong subadditivity and monogamy of mutual information. These results suggest that the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3494","kind":"arxiv","version":4},"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":"2026-05-18T00:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPH0u18vwbZbbtOP3dBqdJhm7lZXuMz49AExSiZiZqnz6GRO+oKX2INvsdIUXUc/C+ON/7qIuSI/i0kQj9ytCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:57:41.751803Z"},"content_sha256":"0dde3ecdc97d9c26a41d260bc5d67d003f2dc5fed8c07febb9d37b57bedbaace","schema_version":"1.0","event_id":"sha256:0dde3ecdc97d9c26a41d260bc5d67d003f2dc5fed8c07febb9d37b57bedbaace"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HT4RXBFMNPXRZ73HGEDMF24KC5/bundle.json","state_url":"https://pith.science/pith/HT4RXBFMNPXRZ73HGEDMF24KC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HT4RXBFMNPXRZ73HGEDMF24KC5/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":"2026-06-10T05:57:41Z","links":{"resolver":"https://pith.science/pith/HT4RXBFMNPXRZ73HGEDMF24KC5","bundle":"https://pith.science/pith/HT4RXBFMNPXRZ73HGEDMF24KC5/bundle.json","state":"https://pith.science/pith/HT4RXBFMNPXRZ73HGEDMF24KC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HT4RXBFMNPXRZ73HGEDMF24KC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HT4RXBFMNPXRZ73HGEDMF24KC5","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":"b70f77aa70bd8f889c62275197af5fb1fd3c7b92938c668f0d2946b8efae4a63","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-11-15T05:16:08Z","title_canon_sha256":"0c19e51ab57c9f230d1888547172852c2319d42e9cc4d3928fdcab3044d5b8a8"},"schema_version":"1.0","source":{"id":"1211.3494","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3494","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3494v4","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3494","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"HT4RXBFMNPXR","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HT4RXBFMNPXRZ73H","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HT4RXBFM","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:0dde3ecdc97d9c26a41d260bc5d67d003f2dc5fed8c07febb9d37b57bedbaace","target":"graph","created_at":"2026-05-18T00:55:47Z","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":"The covariant holographic entropy conjecture of AdS/CFT relates the entropy of a boundary region R to the area of an extremal surface in the bulk spacetime. This extremal surface can be obtained by a maximin construction, allowing many new results to be proven. On manifolds obeying the null curvature condition, these extremal surfaces: i) always lie outside the causal wedge of R, ii) have less area than the bifurcation surface of the causal wedge, iii) move away from the boundary as R grows, and iv) obey strong subadditivity and monogamy of mutual information. These results suggest that the in","authors_text":"Aron C. Wall","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-11-15T05:16:08Z","title":"Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3494","kind":"arxiv","version":4},"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:fe94377d60af4a023e332167d055584acd384e93759bb89c256b35c7540e1965","target":"record","created_at":"2026-05-18T00:55:47Z","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":"b70f77aa70bd8f889c62275197af5fb1fd3c7b92938c668f0d2946b8efae4a63","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-11-15T05:16:08Z","title_canon_sha256":"0c19e51ab57c9f230d1888547172852c2319d42e9cc4d3928fdcab3044d5b8a8"},"schema_version":"1.0","source":{"id":"1211.3494","kind":"arxiv","version":4}},"canonical_sha256":"3cf91b84ac6bef1cff673106c2eb8a1761aa89005496a883b9e80d84b97ebb48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cf91b84ac6bef1cff673106c2eb8a1761aa89005496a883b9e80d84b97ebb48","first_computed_at":"2026-05-18T00:55:47.253728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:47.253728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pZEwXe2R3oqzEatgUWPfSffKQNH2EcP42V4lxYYYqCRhmbWl2i1WWEhu+KgbuqeA5e6j2zD0GO3oJzDwWiCQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:47.254214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3494","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe94377d60af4a023e332167d055584acd384e93759bb89c256b35c7540e1965","sha256:0dde3ecdc97d9c26a41d260bc5d67d003f2dc5fed8c07febb9d37b57bedbaace"],"state_sha256":"4f542d2464c6660368480a202c444b1be8ef91093f276436998c81308f0af579"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uSdpUjtglZF+WyjsyhIumTG9o2QVVmrsEwdZvSKWYfx8wy9ECNBQGDMsoDDgrP4/89KVM2/Eqsdq3dJxdpo0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:57:41.755687Z","bundle_sha256":"7dac0510a8182a199c09bf272879a251721a9a9f9c5143fa2af1affc7c7f9f6c"}}