{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:6UJCIFX3GX7D2MJLW4AEC5HK67","short_pith_number":"pith:6UJCIFX3","canonical_record":{"source":{"id":"2309.14409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-25T18:00:00Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"38a20f94fb3858d3ca47928b6921a460c526c58fc11a98c8a03f6dffde537cd0","abstract_canon_sha256":"eddaba98b661829d611e7bd7898c9a5ebff37ce1ffbe9e1d8cd70df18583b7be"},"schema_version":"1.0"},"canonical_sha256":"f5122416fb35fe3d312bb7004174eaf7fb887a50911f609ff5e2c4d7859806e4","source":{"kind":"arxiv","id":"2309.14409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.14409","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"2309.14409v1","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.14409","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"6UJCIFX3GX7D","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"pith_short_16","alias_value":"6UJCIFX3GX7D2MJL","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"pith_short_8","alias_value":"6UJCIFX3","created_at":"2026-07-05T06:54:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:6UJCIFX3GX7D2MJLW4AEC5HK67","target":"record","payload":{"canonical_record":{"source":{"id":"2309.14409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-25T18:00:00Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"38a20f94fb3858d3ca47928b6921a460c526c58fc11a98c8a03f6dffde537cd0","abstract_canon_sha256":"eddaba98b661829d611e7bd7898c9a5ebff37ce1ffbe9e1d8cd70df18583b7be"},"schema_version":"1.0"},"canonical_sha256":"f5122416fb35fe3d312bb7004174eaf7fb887a50911f609ff5e2c4d7859806e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:54:25.283868Z","signature_b64":"XokMtuhQJ4zcvtf+69RB8AKujX7PPdSjtnQ3ba5yHeaPAl1O0APXeVQmUfoLKhubTCBmNqXuo75tZATBeEa4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5122416fb35fe3d312bb7004174eaf7fb887a50911f609ff5e2c4d7859806e4","last_reissued_at":"2026-07-05T06:54:25.283389Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:54:25.283389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.14409","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":"2026-07-05T06:54:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kZwO2Y22PzTSUxKjKkttIKZCvm+/wi1mSK1uA9fGtbYnR3mYBrrXgKGGT/NAW0GSAZJhLA/Uf5nFH3+QjOigDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:30:12.163010Z"},"content_sha256":"7513de84fd130de0223b0c9a19bcc8d5b15c5e987ee222bb4436940a3f056b48","schema_version":"1.0","event_id":"sha256:7513de84fd130de0223b0c9a19bcc8d5b15c5e987ee222bb4436940a3f056b48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:6UJCIFX3GX7D2MJLW4AEC5HK67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Averaged Null Energy and the Renormalization Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Gr\\'egoire Mathys, Thomas Hartman","submitted_at":"2023-09-25T18:00:00Z","abstract_excerpt":"We establish a connection between the averaged null energy condition (ANEC) and the monotonicity of the renormalization group, by studying the light-ray operator $\\int du T_{uu}$ in quantum field theories that flow between two conformal fixed points. In four dimensions, we derive an exact sum rule relating this operator to the Euler coefficient in the trace anomaly, and show that the ANEC implies the a-theorem. The argument is based on matching anomalies in the stress tensor 3-point function, and relies on special properties of contact terms involving light-ray operators. We also illustrate th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.14409","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/2309.14409/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":"2026-07-05T06:54:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GsZs040oDQ7uG7hPM3A+4pNkbLzoiLxMFHREpFsRuxQi5SaaSdoIYExGUM9RkJzis3ZXcinpysh9rset7P2BBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:30:12.163512Z"},"content_sha256":"b53d51f71cc247dee4d0945c0d1287c8c3bc13acda7a842f7f036158fc99a458","schema_version":"1.0","event_id":"sha256:b53d51f71cc247dee4d0945c0d1287c8c3bc13acda7a842f7f036158fc99a458"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UJCIFX3GX7D2MJLW4AEC5HK67/bundle.json","state_url":"https://pith.science/pith/6UJCIFX3GX7D2MJLW4AEC5HK67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UJCIFX3GX7D2MJLW4AEC5HK67/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":"2026-08-04T00:30:12Z","links":{"resolver":"https://pith.science/pith/6UJCIFX3GX7D2MJLW4AEC5HK67","bundle":"https://pith.science/pith/6UJCIFX3GX7D2MJLW4AEC5HK67/bundle.json","state":"https://pith.science/pith/6UJCIFX3GX7D2MJLW4AEC5HK67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UJCIFX3GX7D2MJLW4AEC5HK67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6UJCIFX3GX7D2MJLW4AEC5HK67","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":"eddaba98b661829d611e7bd7898c9a5ebff37ce1ffbe9e1d8cd70df18583b7be","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-25T18:00:00Z","title_canon_sha256":"38a20f94fb3858d3ca47928b6921a460c526c58fc11a98c8a03f6dffde537cd0"},"schema_version":"1.0","source":{"id":"2309.14409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.14409","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"2309.14409v1","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.14409","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"6UJCIFX3GX7D","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"pith_short_16","alias_value":"6UJCIFX3GX7D2MJL","created_at":"2026-07-05T06:54:25Z"},{"alias_kind":"pith_short_8","alias_value":"6UJCIFX3","created_at":"2026-07-05T06:54:25Z"}],"graph_snapshots":[{"event_id":"sha256:b53d51f71cc247dee4d0945c0d1287c8c3bc13acda7a842f7f036158fc99a458","target":"graph","created_at":"2026-07-05T06:54:25Z","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/2309.14409/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a connection between the averaged null energy condition (ANEC) and the monotonicity of the renormalization group, by studying the light-ray operator $\\int du T_{uu}$ in quantum field theories that flow between two conformal fixed points. In four dimensions, we derive an exact sum rule relating this operator to the Euler coefficient in the trace anomaly, and show that the ANEC implies the a-theorem. The argument is based on matching anomalies in the stress tensor 3-point function, and relies on special properties of contact terms involving light-ray operators. We also illustrate th","authors_text":"Gr\\'egoire Mathys, Thomas Hartman","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-25T18:00:00Z","title":"Averaged Null Energy and the Renormalization Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.14409","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":"sha256:7513de84fd130de0223b0c9a19bcc8d5b15c5e987ee222bb4436940a3f056b48","target":"record","created_at":"2026-07-05T06:54:25Z","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":"eddaba98b661829d611e7bd7898c9a5ebff37ce1ffbe9e1d8cd70df18583b7be","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-25T18:00:00Z","title_canon_sha256":"38a20f94fb3858d3ca47928b6921a460c526c58fc11a98c8a03f6dffde537cd0"},"schema_version":"1.0","source":{"id":"2309.14409","kind":"arxiv","version":1}},"canonical_sha256":"f5122416fb35fe3d312bb7004174eaf7fb887a50911f609ff5e2c4d7859806e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5122416fb35fe3d312bb7004174eaf7fb887a50911f609ff5e2c4d7859806e4","first_computed_at":"2026-07-05T06:54:25.283389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:54:25.283389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XokMtuhQJ4zcvtf+69RB8AKujX7PPdSjtnQ3ba5yHeaPAl1O0APXeVQmUfoLKhubTCBmNqXuo75tZATBeEa4DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:54:25.283868Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.14409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7513de84fd130de0223b0c9a19bcc8d5b15c5e987ee222bb4436940a3f056b48","sha256:b53d51f71cc247dee4d0945c0d1287c8c3bc13acda7a842f7f036158fc99a458"],"state_sha256":"6f5d7ff4ba3b364d8b2b2e9a7a7c41df7c24d749068a9ad275cae93a304f4363"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0LUzX8iPm1mfa/iElMBdVVeivE6bT1+GtYY2UT0f8eMzOJ/XPhBXHQ4L0Ugk+Yl5YzdGX18py1HLPsEnyUnvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T00:30:12.169847Z","bundle_sha256":"c884c2407011d0863aae0594c80e5adbd945d58f0772fdb5abf0897d71c3fce6"}}