{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7TJYT2LROVORG3KWHDRG3TD2JG","short_pith_number":"pith:7TJYT2LR","canonical_record":{"source":{"id":"2105.08173","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-17T21:25:51Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"7b280ed781e3bb35e56c27835fc9012746ae0bde36b475b1c148206277c1c6de","abstract_canon_sha256":"08b7e50891086ff24a4b4db3f36fdfc53b3eef9577c85f0202d28e782dc5350d"},"schema_version":"1.0"},"canonical_sha256":"fcd389e971755d136d5638e26dcc7a49a7bf36cef21e0f073976c767391b2843","source":{"kind":"arxiv","id":"2105.08173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.08173","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"2105.08173v1","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.08173","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"7TJYT2LROVOR","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"7TJYT2LROVORG3KW","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"7TJYT2LR","created_at":"2026-07-05T03:19:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7TJYT2LROVORG3KWHDRG3TD2JG","target":"record","payload":{"canonical_record":{"source":{"id":"2105.08173","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-17T21:25:51Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"7b280ed781e3bb35e56c27835fc9012746ae0bde36b475b1c148206277c1c6de","abstract_canon_sha256":"08b7e50891086ff24a4b4db3f36fdfc53b3eef9577c85f0202d28e782dc5350d"},"schema_version":"1.0"},"canonical_sha256":"fcd389e971755d136d5638e26dcc7a49a7bf36cef21e0f073976c767391b2843","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:19:11.840686Z","signature_b64":"bLlmkAtvDAmTlx2uG9v7Fg+FlFERhiHe6vySSr+pSojWhfH/mXr6Vc6uPvw0IsToaRba1XcUSet+LyrPBUdJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcd389e971755d136d5638e26dcc7a49a7bf36cef21e0f073976c767391b2843","last_reissued_at":"2026-07-05T03:19:11.840212Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:19:11.840212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.08173","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":"2026-07-05T03:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n9tzx/Kj6itQpArQO4zTH+8dLr9XrPSV/FjBnt0cdps2CB/SYusYedbShoqpb1/mLjKhfTtB0iyVysbpM1l8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:16:08.091779Z"},"content_sha256":"941c6be22ba6a4af600c91baa3f7c103c87d776df548e551f2deaa31523cecc1","schema_version":"1.0","event_id":"sha256:941c6be22ba6a4af600c91baa3f7c103c87d776df548e551f2deaa31523cecc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7TJYT2LROVORG3KWHDRG3TD2JG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"N-photon amplitudes in a plane-wave background","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Christian Schubert, James P. Edwards","submitted_at":"2021-05-17T21:25:51Z","abstract_excerpt":"We use the worldline formalism to derive master formulas for the one-loop N-photon amplitudes in a plane-wave background, for both scalar and spinor QED. This generalises previous work by Ilderton and Torgrimsson for the vacuum polarisation case, although with some change in methodology since, instead of evaluating the path integral on the semi-classical trajectory, we use the special kinematics of the plane-wave background to uncover the crypto-gaussian character of this type of worldline path integral."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08173","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/2105.08173/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":"2026-07-05T03:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eoy282vqfhLkvxPiulc40e5RpjH6pEUHdFOAy8eQ9Kd3dotDN+bftXBjXlGjOtLdp6hn8Dn/djbJNQKdZYZeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:16:08.092307Z"},"content_sha256":"5b8446b751d1e640b80fa9ae2ac0739b1dcadd877f45a4c8ec022a806d784c2a","schema_version":"1.0","event_id":"sha256:5b8446b751d1e640b80fa9ae2ac0739b1dcadd877f45a4c8ec022a806d784c2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7TJYT2LROVORG3KWHDRG3TD2JG/bundle.json","state_url":"https://pith.science/pith/7TJYT2LROVORG3KWHDRG3TD2JG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7TJYT2LROVORG3KWHDRG3TD2JG/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":"2026-08-04T04:16:08Z","links":{"resolver":"https://pith.science/pith/7TJYT2LROVORG3KWHDRG3TD2JG","bundle":"https://pith.science/pith/7TJYT2LROVORG3KWHDRG3TD2JG/bundle.json","state":"https://pith.science/pith/7TJYT2LROVORG3KWHDRG3TD2JG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7TJYT2LROVORG3KWHDRG3TD2JG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7TJYT2LROVORG3KWHDRG3TD2JG","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":"08b7e50891086ff24a4b4db3f36fdfc53b3eef9577c85f0202d28e782dc5350d","cross_cats_sorted":["hep-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-17T21:25:51Z","title_canon_sha256":"7b280ed781e3bb35e56c27835fc9012746ae0bde36b475b1c148206277c1c6de"},"schema_version":"1.0","source":{"id":"2105.08173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.08173","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"2105.08173v1","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.08173","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"7TJYT2LROVOR","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"7TJYT2LROVORG3KW","created_at":"2026-07-05T03:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"7TJYT2LR","created_at":"2026-07-05T03:19:11Z"}],"graph_snapshots":[{"event_id":"sha256:5b8446b751d1e640b80fa9ae2ac0739b1dcadd877f45a4c8ec022a806d784c2a","target":"graph","created_at":"2026-07-05T03:19:11Z","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/2105.08173/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use the worldline formalism to derive master formulas for the one-loop N-photon amplitudes in a plane-wave background, for both scalar and spinor QED. This generalises previous work by Ilderton and Torgrimsson for the vacuum polarisation case, although with some change in methodology since, instead of evaluating the path integral on the semi-classical trajectory, we use the special kinematics of the plane-wave background to uncover the crypto-gaussian character of this type of worldline path integral.","authors_text":"Christian Schubert, James P. Edwards","cross_cats":["hep-ph"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-17T21:25:51Z","title":"N-photon amplitudes in a plane-wave background"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08173","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":"sha256:941c6be22ba6a4af600c91baa3f7c103c87d776df548e551f2deaa31523cecc1","target":"record","created_at":"2026-07-05T03:19:11Z","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":"08b7e50891086ff24a4b4db3f36fdfc53b3eef9577c85f0202d28e782dc5350d","cross_cats_sorted":["hep-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-17T21:25:51Z","title_canon_sha256":"7b280ed781e3bb35e56c27835fc9012746ae0bde36b475b1c148206277c1c6de"},"schema_version":"1.0","source":{"id":"2105.08173","kind":"arxiv","version":1}},"canonical_sha256":"fcd389e971755d136d5638e26dcc7a49a7bf36cef21e0f073976c767391b2843","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcd389e971755d136d5638e26dcc7a49a7bf36cef21e0f073976c767391b2843","first_computed_at":"2026-07-05T03:19:11.840212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:19:11.840212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bLlmkAtvDAmTlx2uG9v7Fg+FlFERhiHe6vySSr+pSojWhfH/mXr6Vc6uPvw0IsToaRba1XcUSet+LyrPBUdJDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:19:11.840686Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.08173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:941c6be22ba6a4af600c91baa3f7c103c87d776df548e551f2deaa31523cecc1","sha256:5b8446b751d1e640b80fa9ae2ac0739b1dcadd877f45a4c8ec022a806d784c2a"],"state_sha256":"0744644384423273f75f1024da2ce31e1712c73179a7d592df659b1d7457c36c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZPs/jhcD5fPq3lSgYsMbgKrnA0u5y7cABrbqgqu4zrWMePVcDRdKyGvzQDOnM9/O9eipZzVRV+uXW2CidPdkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:16:08.096480Z","bundle_sha256":"cff51e569a71238e07253e46b87b413caea9a16a31a8b9d454be64a621d5b0bc"}}