{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HZL5QVSBBWZ2QA5PTY4EFQZY56","short_pith_number":"pith:HZL5QVSB","schema_version":"1.0","canonical_sha256":"3e57d856410db3a803af9e3842c338efbd50553ef3db38998676ac96ff9b635a","source":{"kind":"arxiv","id":"1512.06431","version":1},"attestation_state":"computed","paper":{"title":"Relative entropy equals bulk relative entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Aitor Lewkowycz, Daniel L. Jafferis, Juan Maldacena, S. Josephine Suh","submitted_at":"2015-12-20T20:50:58Z","abstract_excerpt":"We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction."},"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":"1512.06431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-20T20:50:58Z","cross_cats_sorted":["gr-qc","quant-ph"],"title_canon_sha256":"bae4718a3f57b46bfb131fbd18efbc7bacd41a690755f9632088c7db217f7768","abstract_canon_sha256":"31f94f8cf5ff241ed43215ef02ec52fb8ddc9f9608277704b568b70df2d61f69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:49.982116Z","signature_b64":"krdj1fLLwM85HD8OIEXZKPIQgl9aGpZcvV27djTDEydBmH7inlMv8r0PzzYtDTGWFdX/OOEzKz9kIo0gsMSrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e57d856410db3a803af9e3842c338efbd50553ef3db38998676ac96ff9b635a","last_reissued_at":"2026-05-18T01:11:49.981754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:49.981754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative entropy equals bulk relative entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Aitor Lewkowycz, Daniel L. Jafferis, Juan Maldacena, S. Josephine Suh","submitted_at":"2015-12-20T20:50:58Z","abstract_excerpt":"We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06431","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":""},"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":"1512.06431","created_at":"2026-05-18T01:11:49.981808+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06431v1","created_at":"2026-05-18T01:11:49.981808+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06431","created_at":"2026-05-18T01:11:49.981808+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZL5QVSBBWZ2","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZL5QVSBBWZ2QA5P","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZL5QVSB","created_at":"2026-05-18T12:29:25.134429+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":16,"internal_anchor_count":14,"sample":[{"citing_arxiv_id":"2605.23670","citing_title":"Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"2309.04231","citing_title":"Subregion Complementarity in AdS/CFT","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2510.25688","citing_title":"Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy","ref_index":47,"is_internal_anchor":true},{"citing_arxiv_id":"2605.16641","citing_title":"On bulk reconstruction in Lorentzian AdS and its flat space limit","ref_index":104,"is_internal_anchor":true},{"citing_arxiv_id":"1911.12333","citing_title":"Replica Wormholes and the Entropy of Hawking Radiation","ref_index":52,"is_internal_anchor":true},{"citing_arxiv_id":"1911.11977","citing_title":"Replica wormholes and the black hole interior","ref_index":37,"is_internal_anchor":true},{"citing_arxiv_id":"1905.08762","citing_title":"The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2510.19939","citing_title":"Covariant phase space and the semi-classical Einstein equation","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2510.20902","citing_title":"Searching for emergent spacetime in spin glasses","ref_index":73,"is_internal_anchor":true},{"citing_arxiv_id":"2511.01978","citing_title":"Single-Sided Black Holes in Double-Scaled SYK Model and No Man's Island","ref_index":69,"is_internal_anchor":true},{"citing_arxiv_id":"2511.02903","citing_title":"Entanglement inequalities, black holes and the architecture of typical states","ref_index":55,"is_internal_anchor":true},{"citing_arxiv_id":"2512.04318","citing_title":"Probing Evaporating Black Holes with Modular Flow in SYK","ref_index":44,"is_internal_anchor":true},{"citing_arxiv_id":"2512.19452","citing_title":"Holographic Tensor Networks as Tessellations of Geometry","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2605.13576","citing_title":"Semiclassical algebraic reconstruction for type III algebras","ref_index":60,"is_internal_anchor":true},{"citing_arxiv_id":"2604.05815","citing_title":"Probing the Factorized Island Branch with the Capacity of Entanglement in JT Gravity","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2604.13163","citing_title":"Covariant phase space approach to noncommutativity in tensile and tensionless open strings","ref_index":49,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56","json":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56.json","graph_json":"https://pith.science/api/pith-number/HZL5QVSBBWZ2QA5PTY4EFQZY56/graph.json","events_json":"https://pith.science/api/pith-number/HZL5QVSBBWZ2QA5PTY4EFQZY56/events.json","paper":"https://pith.science/paper/HZL5QVSB"},"agent_actions":{"view_html":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56","download_json":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56.json","view_paper":"https://pith.science/paper/HZL5QVSB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06431&json=true","fetch_graph":"https://pith.science/api/pith-number/HZL5QVSBBWZ2QA5PTY4EFQZY56/graph.json","fetch_events":"https://pith.science/api/pith-number/HZL5QVSBBWZ2QA5PTY4EFQZY56/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56/action/storage_attestation","attest_author":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56/action/author_attestation","sign_citation":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56/action/citation_signature","submit_replication":"https://pith.science/pith/HZL5QVSBBWZ2QA5PTY4EFQZY56/action/replication_record"}},"created_at":"2026-05-18T01:11:49.981808+00:00","updated_at":"2026-05-18T01:11:49.981808+00:00"}