{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:7B3GMUWPWTZJNUN4IA3AYBICNJ","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":"ddaa6ab1593e3fa4df30586454c1d1c8c7cf409b1dbbd1eda853a8a681bd42b0","cross_cats_sorted":["cond-mat.stat-mech","quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2007-04-27T18:00:44Z","title_canon_sha256":"1ef248a699aa4d81defa5619eb3b3e949d3bd6baf94046a03faa571c1d8c743d"},"schema_version":"1.0","source":{"id":"0704.3719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3719","created_at":"2026-07-04T15:21:46Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3719v1","created_at":"2026-07-04T15:21:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3719","created_at":"2026-07-04T15:21:46Z"},{"alias_kind":"pith_short_12","alias_value":"7B3GMUWPWTZJ","created_at":"2026-07-04T15:21:46Z"},{"alias_kind":"pith_short_16","alias_value":"7B3GMUWPWTZJNUN4","created_at":"2026-07-04T15:21:46Z"},{"alias_kind":"pith_short_8","alias_value":"7B3GMUWP","created_at":"2026-07-04T15:21:46Z"}],"graph_snapshots":[{"event_id":"sha256:0a90694e582b894a7cef68c3129a7d159d20a4d3b217a6a3bc05f5decdfdf0c7","target":"graph","created_at":"2026-07-04T15:21:46Z","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/0704.3719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When a quantum system is divided into subsystems, their entanglement entropies are subject to an inequality known as \"strong subadditivity\". For a field theory this inequality can be stated as follows: given any two regions of space $A$ and $B$, $S(A) + S(B) \\ge S(A \\cup B) + S(A \\cap B)$. Recently, a method has been found for computing entanglement entropies in any field theory for which there is a holographically dual gravity theory. In this note we give a simple geometrical proof of strong subadditivity employing this holographic prescription.","authors_text":"Matthew Headrick, Tadashi Takayanagi","cross_cats":["cond-mat.stat-mech","quant-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2007-04-27T18:00:44Z","title":"A holographic proof of the strong subadditivity of entanglement entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3719","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:fef8d930ac466df455a2fc371afba93b6d8f484f3e3b038afd6366efc6b2be60","target":"record","created_at":"2026-07-04T15:21:46Z","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":"ddaa6ab1593e3fa4df30586454c1d1c8c7cf409b1dbbd1eda853a8a681bd42b0","cross_cats_sorted":["cond-mat.stat-mech","quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2007-04-27T18:00:44Z","title_canon_sha256":"1ef248a699aa4d81defa5619eb3b3e949d3bd6baf94046a03faa571c1d8c743d"},"schema_version":"1.0","source":{"id":"0704.3719","kind":"arxiv","version":1}},"canonical_sha256":"f8766652cfb4f296d1bc40360c05026a5bf0a85d9860fd7455a9a1b954185d68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8766652cfb4f296d1bc40360c05026a5bf0a85d9860fd7455a9a1b954185d68","first_computed_at":"2026-07-04T15:21:46.511676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:21:46.511676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V6pZh0Vcv5QAN/I8+ezKXAN4fYGt8yQRLTBuQGCRUR1+0Vy+ztGiere7rydQnTnOhnsXjB4SRQyL6zee6+hVBg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:21:46.512088Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.3719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fef8d930ac466df455a2fc371afba93b6d8f484f3e3b038afd6366efc6b2be60","sha256:0a90694e582b894a7cef68c3129a7d159d20a4d3b217a6a3bc05f5decdfdf0c7"],"state_sha256":"6b0898d599d6ff35b8f8642c170aa471c19f4427e7d3f4c7bf8b66bfcb06cb31"}