{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:4DAPVJYKJUYGUNUOWUP5HYKK4J","short_pith_number":"pith:4DAPVJYK","canonical_record":{"source":{"id":"hep-th/9803226","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1998-03-26T23:31:43Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"479415a5a73824096859be6e5f4931bcf90f7c6ce5a19db7b3eb36c07bb6d141","abstract_canon_sha256":"9d4d0912ad29ac547741f0b65b624b3a9ab8f662df7c2be827db572e10570669"},"schema_version":"1.0"},"canonical_sha256":"e0c0faa70a4d306a368eb51fd3e14ae2743f89f38a95297fc5f153117833876c","source":{"kind":"arxiv","id":"hep-th/9803226","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9803226","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9803226v3","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9803226","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"4DAPVJYKJUYG","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"4DAPVJYKJUYGUNUO","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"4DAPVJYK","created_at":"2026-07-04T16:09:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:4DAPVJYKJUYGUNUOWUP5HYKK4J","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9803226","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1998-03-26T23:31:43Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"479415a5a73824096859be6e5f4931bcf90f7c6ce5a19db7b3eb36c07bb6d141","abstract_canon_sha256":"9d4d0912ad29ac547741f0b65b624b3a9ab8f662df7c2be827db572e10570669"},"schema_version":"1.0"},"canonical_sha256":"e0c0faa70a4d306a368eb51fd3e14ae2743f89f38a95297fc5f153117833876c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:09:44.667932Z","signature_b64":"uqxSNTUoQvhYsPX4AAvYpZC7m3KtKKEzYggEjf8tqN0Igs11quIPfGz7EkYCRnXcCTeMDKpCvh7xbNBZuWTBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0c0faa70a4d306a368eb51fd3e14ae2743f89f38a95297fc5f153117833876c","last_reissued_at":"2026-07-04T16:09:44.667440Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:09:44.667440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9803226","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":"2026-07-04T16:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iM4qTrDOEeJEK9EtOad+Hg/V+ZMNUH0xQxklEbID4eHVTDPRQNE9RzqCZOfAm9WNGddS92wt/TOyuYh8bPTOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T04:16:56.788072Z"},"content_sha256":"409eea1a008274eb735c3b01bba3268ad9fd682d94bf529dc7d896581b3b767d","schema_version":"1.0","event_id":"sha256:409eea1a008274eb735c3b01bba3268ad9fd682d94bf529dc7d896581b3b767d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:4DAPVJYKJUYGUNUOWUP5HYKK4J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ward-Takahashi Identity with External Field in Ladder QED","license":"","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Efrain J. Ferrer, Vivian de la Incera","submitted_at":"1998-03-26T23:31:43Z","abstract_excerpt":"We derive the Ward-Takahashi identity obeyed by the fermion-antifermion-gauge boson vertex in ladder QED in the presence of a constant magnetic field. The general structure in momentum space of the fermion mass operator with external electromagnetic field is discussed. Using it we find the solutions of the ladder WT identity with magnetic field. The consistency of our results with the solutions of the corresponding Schwinger-Dyson equation ensures the gauge invariance of the magnetic field induced chiral symmetry breaking recently found in ladder QED."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9803226","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/hep-th/9803226/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":"2026-07-04T16:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oqQtTNQumt1V69NA/Pd4NzX7pdG7fhpk67Phf8oZ4v+gszdajVCR1MSMcBLLKjpv3KCI3P75xq9NehLMpHMsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T04:16:56.788453Z"},"content_sha256":"24817262e2e431399b719dbf5907dabd8b4495d7baef995ad0b79c06d022c92c","schema_version":"1.0","event_id":"sha256:24817262e2e431399b719dbf5907dabd8b4495d7baef995ad0b79c06d022c92c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4DAPVJYKJUYGUNUOWUP5HYKK4J/bundle.json","state_url":"https://pith.science/pith/4DAPVJYKJUYGUNUOWUP5HYKK4J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4DAPVJYKJUYGUNUOWUP5HYKK4J/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":"2026-08-18T04:16:56Z","links":{"resolver":"https://pith.science/pith/4DAPVJYKJUYGUNUOWUP5HYKK4J","bundle":"https://pith.science/pith/4DAPVJYKJUYGUNUOWUP5HYKK4J/bundle.json","state":"https://pith.science/pith/4DAPVJYKJUYGUNUOWUP5HYKK4J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4DAPVJYKJUYGUNUOWUP5HYKK4J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:4DAPVJYKJUYGUNUOWUP5HYKK4J","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":"9d4d0912ad29ac547741f0b65b624b3a9ab8f662df7c2be827db572e10570669","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"1998-03-26T23:31:43Z","title_canon_sha256":"479415a5a73824096859be6e5f4931bcf90f7c6ce5a19db7b3eb36c07bb6d141"},"schema_version":"1.0","source":{"id":"hep-th/9803226","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9803226","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9803226v3","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9803226","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"4DAPVJYKJUYG","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"4DAPVJYKJUYGUNUO","created_at":"2026-07-04T16:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"4DAPVJYK","created_at":"2026-07-04T16:09:44Z"}],"graph_snapshots":[{"event_id":"sha256:24817262e2e431399b719dbf5907dabd8b4495d7baef995ad0b79c06d022c92c","target":"graph","created_at":"2026-07-04T16:09:44Z","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/hep-th/9803226/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive the Ward-Takahashi identity obeyed by the fermion-antifermion-gauge boson vertex in ladder QED in the presence of a constant magnetic field. The general structure in momentum space of the fermion mass operator with external electromagnetic field is discussed. Using it we find the solutions of the ladder WT identity with magnetic field. The consistency of our results with the solutions of the corresponding Schwinger-Dyson equation ensures the gauge invariance of the magnetic field induced chiral symmetry breaking recently found in ladder QED.","authors_text":"Efrain J. Ferrer, Vivian de la Incera","cross_cats":["hep-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1998-03-26T23:31:43Z","title":"Ward-Takahashi Identity with External Field in Ladder QED"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9803226","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":"sha256:409eea1a008274eb735c3b01bba3268ad9fd682d94bf529dc7d896581b3b767d","target":"record","created_at":"2026-07-04T16:09:44Z","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":"9d4d0912ad29ac547741f0b65b624b3a9ab8f662df7c2be827db572e10570669","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"1998-03-26T23:31:43Z","title_canon_sha256":"479415a5a73824096859be6e5f4931bcf90f7c6ce5a19db7b3eb36c07bb6d141"},"schema_version":"1.0","source":{"id":"hep-th/9803226","kind":"arxiv","version":3}},"canonical_sha256":"e0c0faa70a4d306a368eb51fd3e14ae2743f89f38a95297fc5f153117833876c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0c0faa70a4d306a368eb51fd3e14ae2743f89f38a95297fc5f153117833876c","first_computed_at":"2026-07-04T16:09:44.667440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:09:44.667440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uqxSNTUoQvhYsPX4AAvYpZC7m3KtKKEzYggEjf8tqN0Igs11quIPfGz7EkYCRnXcCTeMDKpCvh7xbNBZuWTBAg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:09:44.667932Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9803226","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:409eea1a008274eb735c3b01bba3268ad9fd682d94bf529dc7d896581b3b767d","sha256:24817262e2e431399b719dbf5907dabd8b4495d7baef995ad0b79c06d022c92c"],"state_sha256":"28371484a949190da1da5b776c2b01ca71cc79280de9ec60fbdb404e13eb92c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jChn3sUjcuEfXc9qNGPmG4rDNeoyML2e6yX2e/ozXxC3zKs6nirKv9Pm8Aso+wDMKCZf5KHDAsTZEGTfKeJ0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T04:16:56.790978Z","bundle_sha256":"1d42f8decdefe62618b9932142204e215f7fad72443990cacb84d311d150753b"}}