{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:C2MJIMU3H5VMMKJN5FF672HDY6","short_pith_number":"pith:C2MJIMU3","canonical_record":{"source":{"id":"1108.2615","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-12T12:39:25Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"d5b26e4da03d865c3274220f49f1d53f0b863234584af51d318208ccc237fb43","abstract_canon_sha256":"d9b096205c633a7664f219360533351632be38a267789b7b379bb7ec28669d05"},"schema_version":"1.0"},"canonical_sha256":"169894329b3f6ac6292de94befe8e3c79bfcd68b7a1f06b22d37ea4aab758d34","source":{"kind":"arxiv","id":"1108.2615","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2615","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2615v3","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2615","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"C2MJIMU3H5VM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C2MJIMU3H5VMMKJN","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C2MJIMU3","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:C2MJIMU3H5VMMKJN5FF672HDY6","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2615","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-12T12:39:25Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"d5b26e4da03d865c3274220f49f1d53f0b863234584af51d318208ccc237fb43","abstract_canon_sha256":"d9b096205c633a7664f219360533351632be38a267789b7b379bb7ec28669d05"},"schema_version":"1.0"},"canonical_sha256":"169894329b3f6ac6292de94befe8e3c79bfcd68b7a1f06b22d37ea4aab758d34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:35.350267Z","signature_b64":"uSXulnIX/zrMrrDE5Q73H5mOY4fqqQjcUPsGes5G5XROwE0DOfQgOycj7q2k9dwaSHvwEB2D/0IS2Ktc+6k3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"169894329b3f6ac6292de94befe8e3c79bfcd68b7a1f06b22d37ea4aab758d34","last_reissued_at":"2026-05-18T03:12:35.349387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:35.349387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2615","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":"2026-05-18T03:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V7spbImpoVe1zucYZdgLm9r3RIj6lYvvfIAzQitSVe01nhz0ihvxZm7ceU/PFcfMicZvE51Z8NRSWs+nz9wyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:20:47.083827Z"},"content_sha256":"8380c5c8a17153c48423ecc4612487dae1e7e5e6e61a71538e8c651fd8749e21","schema_version":"1.0","event_id":"sha256:8380c5c8a17153c48423ecc4612487dae1e7e5e6e61a71538e8c651fd8749e21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:C2MJIMU3H5VMMKJN5FF672HDY6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pair creation by time-dependent electric fields: Analytic solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Albert Wienczek, Iwo Bialynicki-Birula, {\\L}ukasz Rudnicki","submitted_at":"2011-08-12T12:39:25Z","abstract_excerpt":"Exact analytical solutions are presented for the time evolution of the density of pairs produced in the QED vacuum by a uniform electric field that is adiabatically switched on starting at minus infinity. Pair production is described by the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44, 1825 (1991)]. The explicit solution is obtained by an extension of the method of the spinorial decomposition to deal with a time-varying electric field. The main result of this work is that the pair density is an analytic function of the field strength; it can be expanded into a convergent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2615","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":""},"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":"2026-05-18T03:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m9vniDMOFndEZ8+J039pzHQYwkU+4TOzukBqsAqKA8K+1YPhqNEjhJM1gdAVX62O/s2wyzm2Z5E2a/hw0swRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:20:47.084175Z"},"content_sha256":"079456dd06e80e0438749484fcd8c2e38f3c64acb439d82a6d4a16654e52ac48","schema_version":"1.0","event_id":"sha256:079456dd06e80e0438749484fcd8c2e38f3c64acb439d82a6d4a16654e52ac48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C2MJIMU3H5VMMKJN5FF672HDY6/bundle.json","state_url":"https://pith.science/pith/C2MJIMU3H5VMMKJN5FF672HDY6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C2MJIMU3H5VMMKJN5FF672HDY6/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":"2026-06-02T01:20:47Z","links":{"resolver":"https://pith.science/pith/C2MJIMU3H5VMMKJN5FF672HDY6","bundle":"https://pith.science/pith/C2MJIMU3H5VMMKJN5FF672HDY6/bundle.json","state":"https://pith.science/pith/C2MJIMU3H5VMMKJN5FF672HDY6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C2MJIMU3H5VMMKJN5FF672HDY6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C2MJIMU3H5VMMKJN5FF672HDY6","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":"d9b096205c633a7664f219360533351632be38a267789b7b379bb7ec28669d05","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-12T12:39:25Z","title_canon_sha256":"d5b26e4da03d865c3274220f49f1d53f0b863234584af51d318208ccc237fb43"},"schema_version":"1.0","source":{"id":"1108.2615","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2615","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2615v3","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2615","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"C2MJIMU3H5VM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C2MJIMU3H5VMMKJN","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C2MJIMU3","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:079456dd06e80e0438749484fcd8c2e38f3c64acb439d82a6d4a16654e52ac48","target":"graph","created_at":"2026-05-18T03:12:35Z","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":"Exact analytical solutions are presented for the time evolution of the density of pairs produced in the QED vacuum by a uniform electric field that is adiabatically switched on starting at minus infinity. Pair production is described by the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44, 1825 (1991)]. The explicit solution is obtained by an extension of the method of the spinorial decomposition to deal with a time-varying electric field. The main result of this work is that the pair density is an analytic function of the field strength; it can be expanded into a convergent","authors_text":"Albert Wienczek, Iwo Bialynicki-Birula, {\\L}ukasz Rudnicki","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-12T12:39:25Z","title":"Pair creation by time-dependent electric fields: Analytic solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2615","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":"sha256:8380c5c8a17153c48423ecc4612487dae1e7e5e6e61a71538e8c651fd8749e21","target":"record","created_at":"2026-05-18T03:12:35Z","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":"d9b096205c633a7664f219360533351632be38a267789b7b379bb7ec28669d05","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-12T12:39:25Z","title_canon_sha256":"d5b26e4da03d865c3274220f49f1d53f0b863234584af51d318208ccc237fb43"},"schema_version":"1.0","source":{"id":"1108.2615","kind":"arxiv","version":3}},"canonical_sha256":"169894329b3f6ac6292de94befe8e3c79bfcd68b7a1f06b22d37ea4aab758d34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"169894329b3f6ac6292de94befe8e3c79bfcd68b7a1f06b22d37ea4aab758d34","first_computed_at":"2026-05-18T03:12:35.349387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:35.349387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uSXulnIX/zrMrrDE5Q73H5mOY4fqqQjcUPsGes5G5XROwE0DOfQgOycj7q2k9dwaSHvwEB2D/0IS2Ktc+6k3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:35.350267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2615","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8380c5c8a17153c48423ecc4612487dae1e7e5e6e61a71538e8c651fd8749e21","sha256:079456dd06e80e0438749484fcd8c2e38f3c64acb439d82a6d4a16654e52ac48"],"state_sha256":"1ad8a62da536188e9885a91a4879ec7e923010d499c9442a464c6baec2c1d60a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBfDGe5/L7O8ATcZmQoB37FLZlIpLMLwKPUc1Hkf1x7PaVrEJkk/nvKP12wRU+otsIN2movwfJzwVcZARlzrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:20:47.086818Z","bundle_sha256":"2f495e3d964c3868447610948657c90c1aacd67069a428c2400c8c0cfabc1a60"}}