{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SY5KSO6WX4OD4L5B3GFU3KCFOO","short_pith_number":"pith:SY5KSO6W","canonical_record":{"source":{"id":"1912.01907","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:38:52Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"d51cedad50013cd1774cbe1ef84329ce1abbdefb14ef18058b438d5c03b908a6","abstract_canon_sha256":"a7974f1826af1daf133028cc2e845d33a385c3ebaf888e1cbd3389adf18536a3"},"schema_version":"1.0"},"canonical_sha256":"963aa93bd6bf1c3e2fa1d98b4da845739aa5fb71262cc81c3a619b2c7da60fa4","source":{"kind":"arxiv","id":"1912.01907","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.01907","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"1912.01907v3","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.01907","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"SY5KSO6WX4OD","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"pith_short_16","alias_value":"SY5KSO6WX4OD4L5B","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"pith_short_8","alias_value":"SY5KSO6W","created_at":"2026-07-05T01:18:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SY5KSO6WX4OD4L5B3GFU3KCFOO","target":"record","payload":{"canonical_record":{"source":{"id":"1912.01907","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:38:52Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"d51cedad50013cd1774cbe1ef84329ce1abbdefb14ef18058b438d5c03b908a6","abstract_canon_sha256":"a7974f1826af1daf133028cc2e845d33a385c3ebaf888e1cbd3389adf18536a3"},"schema_version":"1.0"},"canonical_sha256":"963aa93bd6bf1c3e2fa1d98b4da845739aa5fb71262cc81c3a619b2c7da60fa4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:18:43.923042Z","signature_b64":"bf6q6RbuOLzVR28ipIXUAsKJm/G7M0CkHamwwJ3im0GX6dmcfRxNEhOMsd46jPI9EmvzUa5vDxFr3UEke1oCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"963aa93bd6bf1c3e2fa1d98b4da845739aa5fb71262cc81c3a619b2c7da60fa4","last_reissued_at":"2026-07-05T01:18:43.922374Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:18:43.922374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.01907","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:18:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fJz7pM7Y/uYVI1/mwtp23b5KaZ3PChMTy8iYCTEINxUZnfGyviX4IfE6PKaD4vcCBXups5+9FrU1fUOMuyGmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:28:34.162715Z"},"content_sha256":"b16ec1080823cf79674690f8d6575281d1ac74fa15c1eb6fcb970ff0075cea27","schema_version":"1.0","event_id":"sha256:b16ec1080823cf79674690f8d6575281d1ac74fa15c1eb6fcb970ff0075cea27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SY5KSO6WX4OD4L5B3GFU3KCFOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Four-Point Functions in Momentum Space: Conformal Ward Identities in the Scalar/Tensor case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Claudio Corian\\`o, Dimosthenis Theofilopoulos, Matteo Maria Maglio","submitted_at":"2019-12-04T11:38:52Z","abstract_excerpt":"We derive and analyze the conformal Ward identities (CWI's) of a tensor 4-point function of a generic CFT in momentum space. The correlator involves the stress-energy tensor $T$ and three scalar operators $O$ ($TOOO$). We extend the reconstruction method for tensor correlators from 3- to 4-point functions, starting from the transverse traceless sector of the $TOOO$. We derive the structure of the corresponding CWI's in two different sets of variables, relevant for the analysis of the 1-to-3 (1 graviton $\\to$ 3 scalars) and 2-to-2 (graviton + scalar $\\to$ two scalars) scattering processes. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.01907","kind":"arxiv","version":3},"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/1912.01907/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":"2026-07-05T01:18:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H3sz6m/3zYf7OVu5qV51y+mFqVb4T/QpZ7QMlRrDrdMEOc/Sz4sZUcsGkJC6imiTiDKf8EJjWF972pYhyGgnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:28:34.163678Z"},"content_sha256":"8b322c56b709d5f667769524113a013c88342211199cad53bcd814c72e8925a7","schema_version":"1.0","event_id":"sha256:8b322c56b709d5f667769524113a013c88342211199cad53bcd814c72e8925a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SY5KSO6WX4OD4L5B3GFU3KCFOO/bundle.json","state_url":"https://pith.science/pith/SY5KSO6WX4OD4L5B3GFU3KCFOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SY5KSO6WX4OD4L5B3GFU3KCFOO/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":"2026-08-12T14:28:34Z","links":{"resolver":"https://pith.science/pith/SY5KSO6WX4OD4L5B3GFU3KCFOO","bundle":"https://pith.science/pith/SY5KSO6WX4OD4L5B3GFU3KCFOO/bundle.json","state":"https://pith.science/pith/SY5KSO6WX4OD4L5B3GFU3KCFOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SY5KSO6WX4OD4L5B3GFU3KCFOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SY5KSO6WX4OD4L5B3GFU3KCFOO","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":"a7974f1826af1daf133028cc2e845d33a385c3ebaf888e1cbd3389adf18536a3","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:38:52Z","title_canon_sha256":"d51cedad50013cd1774cbe1ef84329ce1abbdefb14ef18058b438d5c03b908a6"},"schema_version":"1.0","source":{"id":"1912.01907","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.01907","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"1912.01907v3","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.01907","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"SY5KSO6WX4OD","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"pith_short_16","alias_value":"SY5KSO6WX4OD4L5B","created_at":"2026-07-05T01:18:43Z"},{"alias_kind":"pith_short_8","alias_value":"SY5KSO6W","created_at":"2026-07-05T01:18:43Z"}],"graph_snapshots":[{"event_id":"sha256:8b322c56b709d5f667769524113a013c88342211199cad53bcd814c72e8925a7","target":"graph","created_at":"2026-07-05T01:18:43Z","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/1912.01907/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive and analyze the conformal Ward identities (CWI's) of a tensor 4-point function of a generic CFT in momentum space. The correlator involves the stress-energy tensor $T$ and three scalar operators $O$ ($TOOO$). We extend the reconstruction method for tensor correlators from 3- to 4-point functions, starting from the transverse traceless sector of the $TOOO$. We derive the structure of the corresponding CWI's in two different sets of variables, relevant for the analysis of the 1-to-3 (1 graviton $\\to$ 3 scalars) and 2-to-2 (graviton + scalar $\\to$ two scalars) scattering processes. The ","authors_text":"Claudio Corian\\`o, Dimosthenis Theofilopoulos, Matteo Maria Maglio","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:38:52Z","title":"Four-Point Functions in Momentum Space: Conformal Ward Identities in the Scalar/Tensor case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.01907","kind":"arxiv","version":3},"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:b16ec1080823cf79674690f8d6575281d1ac74fa15c1eb6fcb970ff0075cea27","target":"record","created_at":"2026-07-05T01:18:43Z","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":"a7974f1826af1daf133028cc2e845d33a385c3ebaf888e1cbd3389adf18536a3","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:38:52Z","title_canon_sha256":"d51cedad50013cd1774cbe1ef84329ce1abbdefb14ef18058b438d5c03b908a6"},"schema_version":"1.0","source":{"id":"1912.01907","kind":"arxiv","version":3}},"canonical_sha256":"963aa93bd6bf1c3e2fa1d98b4da845739aa5fb71262cc81c3a619b2c7da60fa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"963aa93bd6bf1c3e2fa1d98b4da845739aa5fb71262cc81c3a619b2c7da60fa4","first_computed_at":"2026-07-05T01:18:43.922374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:18:43.922374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bf6q6RbuOLzVR28ipIXUAsKJm/G7M0CkHamwwJ3im0GX6dmcfRxNEhOMsd46jPI9EmvzUa5vDxFr3UEke1oCBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:18:43.923042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.01907","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b16ec1080823cf79674690f8d6575281d1ac74fa15c1eb6fcb970ff0075cea27","sha256:8b322c56b709d5f667769524113a013c88342211199cad53bcd814c72e8925a7"],"state_sha256":"650757cc318fd10639e30d716ace9bcda6c2533d5d08489a62342351e7789e80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iIKY+PNUUWRWNYX/DsI9faryffiPYQ2RTucqsQb/FVGZFc1b+zoU8BJPsVDzD2kCghBnTX7QvRMxgj2niODtDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T14:28:34.169451Z","bundle_sha256":"ac49e33855c13f0fcc81823a3fb4a3d599a67351e8877ed85f50fd28cb9ec422"}}