{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PH2CDY35PEYZSDGRRAGCMULPOO","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":"39a8990acb39fbc964d1000a6bf32c1802d82b0dad78b9b6e7850860523f3344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-05T20:34:36Z","title_canon_sha256":"61b32d18b9028902ad512185357d6c25cabb9330103628709693744c28d501ac"},"schema_version":"1.0","source":{"id":"1112.1049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1049","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1049v1","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1049","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"pith_short_12","alias_value":"PH2CDY35PEYZ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PH2CDY35PEYZSDGR","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PH2CDY35","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:18acb74ac02fbf4bb5fe9822fa8c16e9f9f585a0dcb5ee9351213712f39d94ad","target":"graph","created_at":"2026-05-18T01:59:16Z","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"},"paper":{"abstract_excerpt":"We review what is presently known about higher loop corrections to the Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those corrections as a tool for the study of the properties of the QED perturbation series is outlined. As a further step in a long-term effort to prove or disprove the convergence of the N photon amplitudes in the quenched approximation, we present a parameter integral representation of the three-loop Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline formalism.","authors_text":"Christian Schubert, Idrish Huet, Michel Rausch de Traubenberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-05T20:34:36Z","title":"The Euler-Heisenberg Lagrangian beyond one loop"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1049","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:ae09ee49058ba790ad536da58ed54443a744a07de9cbe73fa801b1ec0ba12713","target":"record","created_at":"2026-05-18T01:59:16Z","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":"39a8990acb39fbc964d1000a6bf32c1802d82b0dad78b9b6e7850860523f3344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-05T20:34:36Z","title_canon_sha256":"61b32d18b9028902ad512185357d6c25cabb9330103628709693744c28d501ac"},"schema_version":"1.0","source":{"id":"1112.1049","kind":"arxiv","version":1}},"canonical_sha256":"79f421e37d7931990cd1880c26516f73accaeb45439a2ea50b148f07c8a46cd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79f421e37d7931990cd1880c26516f73accaeb45439a2ea50b148f07c8a46cd3","first_computed_at":"2026-05-18T01:59:16.887253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:16.887253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dcRlH6/63/BthkrC3JCJjiiDs038Gg/b+sa/Rd3xdC3KSpNkACpCa+1vL7Jw0geMvygEifZpV+fpzu/UEaBCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:16.887943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae09ee49058ba790ad536da58ed54443a744a07de9cbe73fa801b1ec0ba12713","sha256:18acb74ac02fbf4bb5fe9822fa8c16e9f9f585a0dcb5ee9351213712f39d94ad"],"state_sha256":"1dde4be83f0fd166af3f20e5f42a92e6a59efe602eeb067d6ca03d1a16f05b8f"}