{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:LMBEXF6TDGLQD4CTTMCK5DJWEA","short_pith_number":"pith:LMBEXF6T","canonical_record":{"source":{"id":"2212.01942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-04T22:28:04Z","cross_cats_sorted":[],"title_canon_sha256":"2807fa298678ec6d093413c6c687131f58aa7f6661a6812f44ec2b5de6e8400d","abstract_canon_sha256":"e4bcc3abb7907ea99f729c0f8f1077327d2148a33e56a2b3b999a10227637be5"},"schema_version":"1.0"},"canonical_sha256":"5b024b97d3199701f0539b04ae8d362024269273959a0e8d5cef0c439a9b595f","source":{"kind":"arxiv","id":"2212.01942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.01942","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"2212.01942v1","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.01942","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"LMBEXF6TDGLQ","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"pith_short_16","alias_value":"LMBEXF6TDGLQD4CT","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"pith_short_8","alias_value":"LMBEXF6T","created_at":"2026-07-05T05:22:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:LMBEXF6TDGLQD4CTTMCK5DJWEA","target":"record","payload":{"canonical_record":{"source":{"id":"2212.01942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-04T22:28:04Z","cross_cats_sorted":[],"title_canon_sha256":"2807fa298678ec6d093413c6c687131f58aa7f6661a6812f44ec2b5de6e8400d","abstract_canon_sha256":"e4bcc3abb7907ea99f729c0f8f1077327d2148a33e56a2b3b999a10227637be5"},"schema_version":"1.0"},"canonical_sha256":"5b024b97d3199701f0539b04ae8d362024269273959a0e8d5cef0c439a9b595f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:22:18.923430Z","signature_b64":"k71BWNGI9+KKMzvQySobMVXxhPHQcjwy+sR3IM81m2UzJEqBPzd7VvyLAImXwb8nCoR4ejK8drFQH84EcR0MDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b024b97d3199701f0539b04ae8d362024269273959a0e8d5cef0c439a9b595f","last_reissued_at":"2026-07-05T05:22:18.923035Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:22:18.923035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.01942","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":"2026-07-05T05:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xe8o2eZlWARBnQL7EOJdC9WfYu+ho+8RE/oB62qxeI2FxXoNjPt7CWUUv3MdacuPWSuqkZGeO6cywdkqZcAvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:06:55.747026Z"},"content_sha256":"b58da2e4f4e7a32ad48fa3b525ea15187f4738684849909856f127bd1c706438","schema_version":"1.0","event_id":"sha256:b58da2e4f4e7a32ad48fa3b525ea15187f4738684849909856f127bd1c706438"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:LMBEXF6TDGLQD4CTTMCK5DJWEA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Focusing bounds for CFT correlators and the S-matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Amirhossein Tajdini, Francesco Sgarlata, Thomas Hartman, Yikun Jiang","submitted_at":"2022-12-04T22:28:04Z","abstract_excerpt":"The focusing theorem in General Relativity underlies causality, singularity theorems, entropy inequalities, and more. In AdS/CFT, we show that focusing in the bulk leads to a bound on CFT $n$-point functions that is generally stronger than causality. Causality is related to the averaged null energy condition (ANEC) on the boundary, while focusing is related to the ANEC in the bulk. The bound is derived by translating the Einstein equations into a relation between bulk and boundary light-ray operators. We also discuss the consequences of focusing for the flat space $S$-matrix, which satisfies a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.01942","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/2212.01942/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":"2026-07-05T05:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0kexnxEVOvm/HOUxTIylsZ/UZQC6srUhgSqpbuYu6Dwp1fERdKM3aLDpo3PzqiDjOWLFe4dpZB/7SvDJL7GKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:06:55.747405Z"},"content_sha256":"ec0a8a7680e8c861079492e1a338c5ccdaf4b54f08516a6605b3e270c3e94023","schema_version":"1.0","event_id":"sha256:ec0a8a7680e8c861079492e1a338c5ccdaf4b54f08516a6605b3e270c3e94023"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LMBEXF6TDGLQD4CTTMCK5DJWEA/bundle.json","state_url":"https://pith.science/pith/LMBEXF6TDGLQD4CTTMCK5DJWEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LMBEXF6TDGLQD4CTTMCK5DJWEA/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":"2026-08-03T18:06:55Z","links":{"resolver":"https://pith.science/pith/LMBEXF6TDGLQD4CTTMCK5DJWEA","bundle":"https://pith.science/pith/LMBEXF6TDGLQD4CTTMCK5DJWEA/bundle.json","state":"https://pith.science/pith/LMBEXF6TDGLQD4CTTMCK5DJWEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LMBEXF6TDGLQD4CTTMCK5DJWEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:LMBEXF6TDGLQD4CTTMCK5DJWEA","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":"e4bcc3abb7907ea99f729c0f8f1077327d2148a33e56a2b3b999a10227637be5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-04T22:28:04Z","title_canon_sha256":"2807fa298678ec6d093413c6c687131f58aa7f6661a6812f44ec2b5de6e8400d"},"schema_version":"1.0","source":{"id":"2212.01942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.01942","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"2212.01942v1","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.01942","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"LMBEXF6TDGLQ","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"pith_short_16","alias_value":"LMBEXF6TDGLQD4CT","created_at":"2026-07-05T05:22:18Z"},{"alias_kind":"pith_short_8","alias_value":"LMBEXF6T","created_at":"2026-07-05T05:22:18Z"}],"graph_snapshots":[{"event_id":"sha256:ec0a8a7680e8c861079492e1a338c5ccdaf4b54f08516a6605b3e270c3e94023","target":"graph","created_at":"2026-07-05T05:22:18Z","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/2212.01942/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The focusing theorem in General Relativity underlies causality, singularity theorems, entropy inequalities, and more. In AdS/CFT, we show that focusing in the bulk leads to a bound on CFT $n$-point functions that is generally stronger than causality. Causality is related to the averaged null energy condition (ANEC) on the boundary, while focusing is related to the ANEC in the bulk. The bound is derived by translating the Einstein equations into a relation between bulk and boundary light-ray operators. We also discuss the consequences of focusing for the flat space $S$-matrix, which satisfies a","authors_text":"Amirhossein Tajdini, Francesco Sgarlata, Thomas Hartman, Yikun Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-04T22:28:04Z","title":"Focusing bounds for CFT correlators and the S-matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.01942","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:b58da2e4f4e7a32ad48fa3b525ea15187f4738684849909856f127bd1c706438","target":"record","created_at":"2026-07-05T05:22:18Z","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":"e4bcc3abb7907ea99f729c0f8f1077327d2148a33e56a2b3b999a10227637be5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-04T22:28:04Z","title_canon_sha256":"2807fa298678ec6d093413c6c687131f58aa7f6661a6812f44ec2b5de6e8400d"},"schema_version":"1.0","source":{"id":"2212.01942","kind":"arxiv","version":1}},"canonical_sha256":"5b024b97d3199701f0539b04ae8d362024269273959a0e8d5cef0c439a9b595f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b024b97d3199701f0539b04ae8d362024269273959a0e8d5cef0c439a9b595f","first_computed_at":"2026-07-05T05:22:18.923035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:22:18.923035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k71BWNGI9+KKMzvQySobMVXxhPHQcjwy+sR3IM81m2UzJEqBPzd7VvyLAImXwb8nCoR4ejK8drFQH84EcR0MDA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:22:18.923430Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.01942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b58da2e4f4e7a32ad48fa3b525ea15187f4738684849909856f127bd1c706438","sha256:ec0a8a7680e8c861079492e1a338c5ccdaf4b54f08516a6605b3e270c3e94023"],"state_sha256":"f0254a08839fa7a5ce1bffda1e832ea7f6c39411cee9778ce3476866c48465b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WEoJ4UGH7j2pybKAmy2VW6bXZdLuPu2sdUtKOeL0io40qQOVO4f7SiJFvbX+UqjgiEt1lQlMISqJlJMmDYUHCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:06:55.750051Z","bundle_sha256":"792ac1c3dbfc9beccd7617807500817e10bf8c327bbe58a6dfd5b46f46eaa6f5"}}