{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:PUG6DURBLXS4HGDCCEXX6KXYXS","short_pith_number":"pith:PUG6DURB","canonical_record":{"source":{"id":"hep-th/9902064","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-02-09T13:51:02Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"3fa5f86debd97b55b973da4922fe39c5373fbd7e39cd8d86feb06840483869ee","abstract_canon_sha256":"839e7446119dfcb84af030c431f30525601ef306aa9d72ce6dfd79de0088a047"},"schema_version":"1.0"},"canonical_sha256":"7d0de1d2215de5c39862112f7f2af8bcbdf46fb3a8dafa505bcd5b42641a22b8","source":{"kind":"arxiv","id":"hep-th/9902064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9902064","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9902064v1","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9902064","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_12","alias_value":"PUG6DURBLXS4","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_16","alias_value":"PUG6DURBLXS4HGDC","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_8","alias_value":"PUG6DURB","created_at":"2026-07-04T16:14:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:PUG6DURBLXS4HGDCCEXX6KXYXS","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9902064","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-02-09T13:51:02Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"3fa5f86debd97b55b973da4922fe39c5373fbd7e39cd8d86feb06840483869ee","abstract_canon_sha256":"839e7446119dfcb84af030c431f30525601ef306aa9d72ce6dfd79de0088a047"},"schema_version":"1.0"},"canonical_sha256":"7d0de1d2215de5c39862112f7f2af8bcbdf46fb3a8dafa505bcd5b42641a22b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:14:44.894521Z","signature_b64":"fWzvdezCFR6Ij7833dlhpaG3bFipQR3N0YBD7kxVaObrqkmZUbrAFjD3ZdeGY181whOPaeeeA8yHHJ6tLp+jDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d0de1d2215de5c39862112f7f2af8bcbdf46fb3a8dafa505bcd5b42641a22b8","last_reissued_at":"2026-07-04T16:14:44.894108Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:14:44.894108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9902064","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":"2026-07-04T16:14:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PKRGVmKVZajkQU+q6gleQnwLEfGFVu34SxtxaNZaotnVS1yXqa8zat3w9E59GWKtK8B8zlJfLHYJMB5a6X5ZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:04:13.294804Z"},"content_sha256":"557d6f93c0652556f3a212d57ae3f510e88fe5b8d68edefeeb7dd4abba0c17a8","schema_version":"1.0","event_id":"sha256:557d6f93c0652556f3a212d57ae3f510e88fe5b8d68edefeeb7dd4abba0c17a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:PUG6DURBLXS4HGDCCEXX6KXYXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Borel Summation of the Derivative Expansion and Effective Actions","license":"","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Gerald V. Dunne, Theodore M. Hall","submitted_at":"1999-02-09T13:51:02Z","abstract_excerpt":"We give an explicit demonstration that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B\\to iE gives a non-Borel-summable perturbative series for a time dependent background electric field, and Borel dispersion relations yield the non-perturbative imaginary part of the effective action, which determines the pair production probability. Resummations of leading Borel approximations exponentiate to give perturbative corrections to the exponents in the non-pe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9902064","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/hep-th/9902064/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":"2026-07-04T16:14:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d0j7wDhsH1+dqT21Mc0nVRgrdJZPmuc2NrN03hSni8ckApmAmc+YWKnLMnNcy4imyX4pzeuU1R79GmoHChizBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:04:13.295322Z"},"content_sha256":"b71e1325021353aa8c8c5b17e8efcaf31871616ff1fd37b0b9de2e503970a1fa","schema_version":"1.0","event_id":"sha256:b71e1325021353aa8c8c5b17e8efcaf31871616ff1fd37b0b9de2e503970a1fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PUG6DURBLXS4HGDCCEXX6KXYXS/bundle.json","state_url":"https://pith.science/pith/PUG6DURBLXS4HGDCCEXX6KXYXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PUG6DURBLXS4HGDCCEXX6KXYXS/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":"2026-08-03T22:04:13Z","links":{"resolver":"https://pith.science/pith/PUG6DURBLXS4HGDCCEXX6KXYXS","bundle":"https://pith.science/pith/PUG6DURBLXS4HGDCCEXX6KXYXS/bundle.json","state":"https://pith.science/pith/PUG6DURBLXS4HGDCCEXX6KXYXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PUG6DURBLXS4HGDCCEXX6KXYXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:PUG6DURBLXS4HGDCCEXX6KXYXS","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":"839e7446119dfcb84af030c431f30525601ef306aa9d72ce6dfd79de0088a047","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"1999-02-09T13:51:02Z","title_canon_sha256":"3fa5f86debd97b55b973da4922fe39c5373fbd7e39cd8d86feb06840483869ee"},"schema_version":"1.0","source":{"id":"hep-th/9902064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9902064","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9902064v1","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9902064","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_12","alias_value":"PUG6DURBLXS4","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_16","alias_value":"PUG6DURBLXS4HGDC","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_8","alias_value":"PUG6DURB","created_at":"2026-07-04T16:14:44Z"}],"graph_snapshots":[{"event_id":"sha256:b71e1325021353aa8c8c5b17e8efcaf31871616ff1fd37b0b9de2e503970a1fa","target":"graph","created_at":"2026-07-04T16:14:44Z","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/9902064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an explicit demonstration that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B\\to iE gives a non-Borel-summable perturbative series for a time dependent background electric field, and Borel dispersion relations yield the non-perturbative imaginary part of the effective action, which determines the pair production probability. Resummations of leading Borel approximations exponentiate to give perturbative corrections to the exponents in the non-pe","authors_text":"Gerald V. Dunne, Theodore M. Hall","cross_cats":["hep-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-02-09T13:51:02Z","title":"Borel Summation of the Derivative Expansion and Effective Actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9902064","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":"sha256:557d6f93c0652556f3a212d57ae3f510e88fe5b8d68edefeeb7dd4abba0c17a8","target":"record","created_at":"2026-07-04T16:14:44Z","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":"839e7446119dfcb84af030c431f30525601ef306aa9d72ce6dfd79de0088a047","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"1999-02-09T13:51:02Z","title_canon_sha256":"3fa5f86debd97b55b973da4922fe39c5373fbd7e39cd8d86feb06840483869ee"},"schema_version":"1.0","source":{"id":"hep-th/9902064","kind":"arxiv","version":1}},"canonical_sha256":"7d0de1d2215de5c39862112f7f2af8bcbdf46fb3a8dafa505bcd5b42641a22b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d0de1d2215de5c39862112f7f2af8bcbdf46fb3a8dafa505bcd5b42641a22b8","first_computed_at":"2026-07-04T16:14:44.894108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:14:44.894108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fWzvdezCFR6Ij7833dlhpaG3bFipQR3N0YBD7kxVaObrqkmZUbrAFjD3ZdeGY181whOPaeeeA8yHHJ6tLp+jDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:14:44.894521Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9902064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:557d6f93c0652556f3a212d57ae3f510e88fe5b8d68edefeeb7dd4abba0c17a8","sha256:b71e1325021353aa8c8c5b17e8efcaf31871616ff1fd37b0b9de2e503970a1fa"],"state_sha256":"59c51650a0aebdf11713d610f19b3dcd020b67165bb337fc96ad7510856f1f11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vI0pLjUN90q4W6bPAgmvPpiAoslvglMnsskD0ooCx2AjzyqJxsivE97erWq19Is4u24kP1FZ6jRcQOCCWw+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:04:13.300924Z","bundle_sha256":"28efe2a2c4b10dc1f8124bdcba13075b3b9d77028ef40f9c2061324de950e42a"}}