{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ANQGNVPZY667QVWA723J5TEVIY","short_pith_number":"pith:ANQGNVPZ","canonical_record":{"source":{"id":"2402.04120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-02-06T16:12:44Z","cross_cats_sorted":[],"title_canon_sha256":"7ce15b3372374fb86cc1dbf5b8c04c3d75a773b276874ba94fd8d2d79766c587","abstract_canon_sha256":"09e4addc8febb72f9e2f8f9f6ed70677be62ab36a00910ba498c8721ce0e0f33"},"schema_version":"1.0"},"canonical_sha256":"036066d5f9c7bdf856c0feb69ecc954605d2b7c4e608f4b81f253867fc860d4c","source":{"kind":"arxiv","id":"2402.04120","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.04120","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"2402.04120v2","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.04120","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"ANQGNVPZY667","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"pith_short_16","alias_value":"ANQGNVPZY667QVWA","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"pith_short_8","alias_value":"ANQGNVPZ","created_at":"2026-07-05T08:50:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ANQGNVPZY667QVWA723J5TEVIY","target":"record","payload":{"canonical_record":{"source":{"id":"2402.04120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-02-06T16:12:44Z","cross_cats_sorted":[],"title_canon_sha256":"7ce15b3372374fb86cc1dbf5b8c04c3d75a773b276874ba94fd8d2d79766c587","abstract_canon_sha256":"09e4addc8febb72f9e2f8f9f6ed70677be62ab36a00910ba498c8721ce0e0f33"},"schema_version":"1.0"},"canonical_sha256":"036066d5f9c7bdf856c0feb69ecc954605d2b7c4e608f4b81f253867fc860d4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:50:09.580409Z","signature_b64":"yWLH8EqWl4sZc3SnRVoEqtTa4/AuxuitpM47ytBTquHrhzHSjgTgIJEoDZP14h+6ihx+Wbi7S40WdfKNOeF8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"036066d5f9c7bdf856c0feb69ecc954605d2b7c4e608f4b81f253867fc860d4c","last_reissued_at":"2026-07-05T08:50:09.579982Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:50:09.579982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.04120","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLx37kySv8Xihc9W/qCsqwkbnN43dN3iRFymDpDme8fFouYT1YInYCAdkzOm5g6NL1NKFRkUrpoykKuCTsHRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T17:05:24.041282Z"},"content_sha256":"17f905ef17decd6ff6d6985afa1b485c41aaccc44f0b5c6df006c6a865aa75d7","schema_version":"1.0","event_id":"sha256:17f905ef17decd6ff6d6985afa1b485c41aaccc44f0b5c6df006c6a865aa75d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ANQGNVPZY667QVWA723J5TEVIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Feynman rules and loop structure of Carrollian amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Jiang Long, Wen-Bin Liu, Xiao-Quan Ye","submitted_at":"2024-02-06T16:12:44Z","abstract_excerpt":"In this paper, we derive the Carrollian amplitude in the framework of bulk reduction. The Carrollian amplitude is shown to relate to the scattering amplitude by a Fourier transform in this method. We propose Feynman rules to calculate the Carrollian amplitude where the Fourier transforms emerge as the integral representation of the external lines in the Carrollian space. Then we study the four-point Carrollian amplitude at loop level in massless $\\Phi^4$ theory. As a consequence of Poincar\\'e invariance, the four-point Carrollian amplitude can be transformed to the amplitude that only depends "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04120","kind":"arxiv","version":2},"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/2402.04120/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":"2026-07-05T08:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/HpSTNUwTrq4BozQvFB50FtC5AJIG0ZABtQMv8tCHVsOvELYgSR+l5Y+f5Af1JXwMkk1N8Dlcz4BA/fkc2wCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T17:05:24.041802Z"},"content_sha256":"42af586e808ed19e70b9eb6d1b83db7e36c93e421738c4dc265e0e9aa0b8d33b","schema_version":"1.0","event_id":"sha256:42af586e808ed19e70b9eb6d1b83db7e36c93e421738c4dc265e0e9aa0b8d33b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ANQGNVPZY667QVWA723J5TEVIY/bundle.json","state_url":"https://pith.science/pith/ANQGNVPZY667QVWA723J5TEVIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ANQGNVPZY667QVWA723J5TEVIY/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":"2026-08-20T17:05:24Z","links":{"resolver":"https://pith.science/pith/ANQGNVPZY667QVWA723J5TEVIY","bundle":"https://pith.science/pith/ANQGNVPZY667QVWA723J5TEVIY/bundle.json","state":"https://pith.science/pith/ANQGNVPZY667QVWA723J5TEVIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ANQGNVPZY667QVWA723J5TEVIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ANQGNVPZY667QVWA723J5TEVIY","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":"09e4addc8febb72f9e2f8f9f6ed70677be62ab36a00910ba498c8721ce0e0f33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-02-06T16:12:44Z","title_canon_sha256":"7ce15b3372374fb86cc1dbf5b8c04c3d75a773b276874ba94fd8d2d79766c587"},"schema_version":"1.0","source":{"id":"2402.04120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.04120","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"2402.04120v2","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.04120","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"ANQGNVPZY667","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"pith_short_16","alias_value":"ANQGNVPZY667QVWA","created_at":"2026-07-05T08:50:09Z"},{"alias_kind":"pith_short_8","alias_value":"ANQGNVPZ","created_at":"2026-07-05T08:50:09Z"}],"graph_snapshots":[{"event_id":"sha256:42af586e808ed19e70b9eb6d1b83db7e36c93e421738c4dc265e0e9aa0b8d33b","target":"graph","created_at":"2026-07-05T08:50:09Z","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/2402.04120/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we derive the Carrollian amplitude in the framework of bulk reduction. The Carrollian amplitude is shown to relate to the scattering amplitude by a Fourier transform in this method. We propose Feynman rules to calculate the Carrollian amplitude where the Fourier transforms emerge as the integral representation of the external lines in the Carrollian space. Then we study the four-point Carrollian amplitude at loop level in massless $\\Phi^4$ theory. As a consequence of Poincar\\'e invariance, the four-point Carrollian amplitude can be transformed to the amplitude that only depends ","authors_text":"Jiang Long, Wen-Bin Liu, Xiao-Quan Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-02-06T16:12:44Z","title":"Feynman rules and loop structure of Carrollian amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04120","kind":"arxiv","version":2},"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":"sha256:17f905ef17decd6ff6d6985afa1b485c41aaccc44f0b5c6df006c6a865aa75d7","target":"record","created_at":"2026-07-05T08:50:09Z","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":"09e4addc8febb72f9e2f8f9f6ed70677be62ab36a00910ba498c8721ce0e0f33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-02-06T16:12:44Z","title_canon_sha256":"7ce15b3372374fb86cc1dbf5b8c04c3d75a773b276874ba94fd8d2d79766c587"},"schema_version":"1.0","source":{"id":"2402.04120","kind":"arxiv","version":2}},"canonical_sha256":"036066d5f9c7bdf856c0feb69ecc954605d2b7c4e608f4b81f253867fc860d4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"036066d5f9c7bdf856c0feb69ecc954605d2b7c4e608f4b81f253867fc860d4c","first_computed_at":"2026-07-05T08:50:09.579982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:50:09.579982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yWLH8EqWl4sZc3SnRVoEqtTa4/AuxuitpM47ytBTquHrhzHSjgTgIJEoDZP14h+6ihx+Wbi7S40WdfKNOeF8Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:50:09.580409Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.04120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17f905ef17decd6ff6d6985afa1b485c41aaccc44f0b5c6df006c6a865aa75d7","sha256:42af586e808ed19e70b9eb6d1b83db7e36c93e421738c4dc265e0e9aa0b8d33b"],"state_sha256":"08c5f024df9b734200aa0077c6c04cad945552e75d037c389cc228e1409ee913"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4MEbBhxW/dTu66vCKYcBf0dGTRRszfr08W7vL1V4pOQ4fhw9Ulb0BwRh+Ruc+Z0NCE72ypU8qksDFlWMZN4yDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T17:05:24.046739Z","bundle_sha256":"84636d5669abaa4befd7f1c0bb7bbe18b343e0e951e5246ea112f50c9ca18ef8"}}