{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:VMEG2ZMQMW5GNO7LYGYX7F7CR7","short_pith_number":"pith:VMEG2ZMQ","canonical_record":{"source":{"id":"hep-th/0701047","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-01-08T00:48:02Z","cross_cats_sorted":["astro-ph","hep-ph","nucl-th"],"title_canon_sha256":"3acf8ada5bdd2781b500a7f90a322f4ffa7558e78c6084c488b9c2a63418dd40","abstract_canon_sha256":"a89697146a692344c457f677afc6be5b428908e2dcec246e9470dc4a1272ecb3"},"schema_version":"1.0"},"canonical_sha256":"ab086d659065ba66bbebc1b17f97e28fe42e456b4707707737a205f4659ea518","source":{"kind":"arxiv","id":"hep-th/0701047","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0701047","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0701047v3","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0701047","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"VMEG2ZMQMW5G","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"pith_short_16","alias_value":"VMEG2ZMQMW5GNO7L","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"pith_short_8","alias_value":"VMEG2ZMQ","created_at":"2026-07-04T15:22:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:VMEG2ZMQMW5GNO7LYGYX7F7CR7","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0701047","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-01-08T00:48:02Z","cross_cats_sorted":["astro-ph","hep-ph","nucl-th"],"title_canon_sha256":"3acf8ada5bdd2781b500a7f90a322f4ffa7558e78c6084c488b9c2a63418dd40","abstract_canon_sha256":"a89697146a692344c457f677afc6be5b428908e2dcec246e9470dc4a1272ecb3"},"schema_version":"1.0"},"canonical_sha256":"ab086d659065ba66bbebc1b17f97e28fe42e456b4707707737a205f4659ea518","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:22:11.108827Z","signature_b64":"r9Er4vkffwxax+hAlHfRjAAIgg6/Dol0usUqyqJoo1+XQrrkdpGf9qLWdWYLZFICcbNZr3wXyQ+xU4TLXF+OCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab086d659065ba66bbebc1b17f97e28fe42e456b4707707737a205f4659ea518","last_reissued_at":"2026-07-04T15:22:11.108435Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:22:11.108435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0701047","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":"2026-07-04T15:22:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bFKADGUZsbM2td1zqBF7GeUTQu0NyIFCBKhC01Oh3jtPj+Tf2396qpf12HwWqcwdplRip+kRBymKODvxSpN1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:10:10.338882Z"},"content_sha256":"d2b62fd3434118f22d7b4e28865adbe4e8a3c4ff2f04253d3eb269ded85e9ec1","schema_version":"1.0","event_id":"sha256:d2b62fd3434118f22d7b4e28865adbe4e8a3c4ff2f04253d3eb269ded85e9ec1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:VMEG2ZMQMW5GNO7LYGYX7F7CR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields","license":"","headline":"","cross_cats":["astro-ph","hep-ph","nucl-th"],"primary_cat":"hep-th","authors_text":"Don N. Page, Sang Pyo Kim","submitted_at":"2007-01-08T00:48:02Z","abstract_excerpt":"Reformulating the instantons in a complex plane for tunneling or transmitting states, we calculate the pair-production rate of charged fermions in a spatially localized electric field, illustrated by the Sauter electric field E_0 sech^2 (z/L), and in a temporally localized electric field such as E_0 sech^2 (t/T). The integration of the quadratic part of WKB instanton actions over the frequency and transverse momentum leads to the pair-production rate obtained by the worldline instanton method, including the prefactor, of Phys. Rev. D72, 105004 (2005) and D73, 065028 (2006). It is further shown"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0701047","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/0701047/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":"2026-07-04T15:22:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJ6YjD26vV7B53gKo44Ifo8vkHjQoCLXH1OBdsjznQFCBNLTp6lZ6ku/oV6bor8ZSCTwvC8gfxtKUbDAxZghAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:10:10.339870Z"},"content_sha256":"a7ad65b8f8d2b66cf14665464f248aded5e46b5957646628e7f892112d723378","schema_version":"1.0","event_id":"sha256:a7ad65b8f8d2b66cf14665464f248aded5e46b5957646628e7f892112d723378"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VMEG2ZMQMW5GNO7LYGYX7F7CR7/bundle.json","state_url":"https://pith.science/pith/VMEG2ZMQMW5GNO7LYGYX7F7CR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VMEG2ZMQMW5GNO7LYGYX7F7CR7/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":"2026-08-17T08:10:10Z","links":{"resolver":"https://pith.science/pith/VMEG2ZMQMW5GNO7LYGYX7F7CR7","bundle":"https://pith.science/pith/VMEG2ZMQMW5GNO7LYGYX7F7CR7/bundle.json","state":"https://pith.science/pith/VMEG2ZMQMW5GNO7LYGYX7F7CR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VMEG2ZMQMW5GNO7LYGYX7F7CR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:VMEG2ZMQMW5GNO7LYGYX7F7CR7","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":"a89697146a692344c457f677afc6be5b428908e2dcec246e9470dc4a1272ecb3","cross_cats_sorted":["astro-ph","hep-ph","nucl-th"],"license":"","primary_cat":"hep-th","submitted_at":"2007-01-08T00:48:02Z","title_canon_sha256":"3acf8ada5bdd2781b500a7f90a322f4ffa7558e78c6084c488b9c2a63418dd40"},"schema_version":"1.0","source":{"id":"hep-th/0701047","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0701047","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0701047v3","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0701047","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"VMEG2ZMQMW5G","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"pith_short_16","alias_value":"VMEG2ZMQMW5GNO7L","created_at":"2026-07-04T15:22:11Z"},{"alias_kind":"pith_short_8","alias_value":"VMEG2ZMQ","created_at":"2026-07-04T15:22:11Z"}],"graph_snapshots":[{"event_id":"sha256:a7ad65b8f8d2b66cf14665464f248aded5e46b5957646628e7f892112d723378","target":"graph","created_at":"2026-07-04T15:22:11Z","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/hep-th/0701047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Reformulating the instantons in a complex plane for tunneling or transmitting states, we calculate the pair-production rate of charged fermions in a spatially localized electric field, illustrated by the Sauter electric field E_0 sech^2 (z/L), and in a temporally localized electric field such as E_0 sech^2 (t/T). The integration of the quadratic part of WKB instanton actions over the frequency and transverse momentum leads to the pair-production rate obtained by the worldline instanton method, including the prefactor, of Phys. Rev. D72, 105004 (2005) and D73, 065028 (2006). It is further shown","authors_text":"Don N. Page, Sang Pyo Kim","cross_cats":["astro-ph","hep-ph","nucl-th"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2007-01-08T00:48:02Z","title":"Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0701047","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:d2b62fd3434118f22d7b4e28865adbe4e8a3c4ff2f04253d3eb269ded85e9ec1","target":"record","created_at":"2026-07-04T15:22:11Z","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":"a89697146a692344c457f677afc6be5b428908e2dcec246e9470dc4a1272ecb3","cross_cats_sorted":["astro-ph","hep-ph","nucl-th"],"license":"","primary_cat":"hep-th","submitted_at":"2007-01-08T00:48:02Z","title_canon_sha256":"3acf8ada5bdd2781b500a7f90a322f4ffa7558e78c6084c488b9c2a63418dd40"},"schema_version":"1.0","source":{"id":"hep-th/0701047","kind":"arxiv","version":3}},"canonical_sha256":"ab086d659065ba66bbebc1b17f97e28fe42e456b4707707737a205f4659ea518","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab086d659065ba66bbebc1b17f97e28fe42e456b4707707737a205f4659ea518","first_computed_at":"2026-07-04T15:22:11.108435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:22:11.108435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r9Er4vkffwxax+hAlHfRjAAIgg6/Dol0usUqyqJoo1+XQrrkdpGf9qLWdWYLZFICcbNZr3wXyQ+xU4TLXF+OCA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:22:11.108827Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0701047","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2b62fd3434118f22d7b4e28865adbe4e8a3c4ff2f04253d3eb269ded85e9ec1","sha256:a7ad65b8f8d2b66cf14665464f248aded5e46b5957646628e7f892112d723378"],"state_sha256":"48f3e566c4c38d6c98447f1ab9e4e6790d20dc2c87adad3729c3289c5c881df6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+fsBVNzetmljF5VAaRAu/Uwug3HJorUqUWwmvsG0gAhb9/fBgqxa9oiSXx9N3jsdPjjBxjpopnWSloHTR/pBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T08:10:10.345861Z","bundle_sha256":"41e75c999aaf098ae85e473acaca7edaef16c25aa018193924594882decdb3fb"}}