{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7CQMVDAOG4TVFHUKGZ6OGMVRUA","short_pith_number":"pith:7CQMVDAO","canonical_record":{"source":{"id":"1007.1099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-07-07T10:34:10Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"6a590919c67854cdc36cc49046c9cf2b4e9183195647cf6b509f0d114f9827b5","abstract_canon_sha256":"4e6a347cc5dfd1a0e235eaa76e9637d131cbe58bc376811eb7c2a07ba758f300"},"schema_version":"1.0"},"canonical_sha256":"f8a0ca8c0e3727529e8a367ce332b1a0223b1a49b4f0aef23faab881d4c35fce","source":{"kind":"arxiv","id":"1007.1099","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1099","created_at":"2026-05-18T04:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1099v2","created_at":"2026-05-18T04:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1099","created_at":"2026-05-18T04:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"7CQMVDAOG4TV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7CQMVDAOG4TVFHUK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7CQMVDAO","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7CQMVDAOG4TVFHUKGZ6OGMVRUA","target":"record","payload":{"canonical_record":{"source":{"id":"1007.1099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-07-07T10:34:10Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"6a590919c67854cdc36cc49046c9cf2b4e9183195647cf6b509f0d114f9827b5","abstract_canon_sha256":"4e6a347cc5dfd1a0e235eaa76e9637d131cbe58bc376811eb7c2a07ba758f300"},"schema_version":"1.0"},"canonical_sha256":"f8a0ca8c0e3727529e8a367ce332b1a0223b1a49b4f0aef23faab881d4c35fce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:46.209383Z","signature_b64":"0wP4x7uuQeR9sXWvD+8JPSFn56oU6+hN2wyO7sUfjusJaupJNCupxHrzOvjcvnncOs/40G6sRf6MgpLQ+94VDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8a0ca8c0e3727529e8a367ce332b1a0223b1a49b4f0aef23faab881d4c35fce","last_reissued_at":"2026-05-18T04:32:46.208925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:46.208925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.1099","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L6Wlh8mpho6WFLAx6Va5jfJB6S76iyyEjumnsdPb/2W2G87WTJ/L40/TR4BTduUCgyOggex/yx54+m5YEmB0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T11:17:01.921901Z"},"content_sha256":"b5c14abc28cee98a4ad3e6468152d569920d992f2dc0592345777c37ff749db3","schema_version":"1.0","event_id":"sha256:b5c14abc28cee98a4ad3e6468152d569920d992f2dc0592345777c37ff749db3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7CQMVDAOG4TVFHUKGZ6OGMVRUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Florian Hebenstreit, Holger Gies, Reinhard Alkofer","submitted_at":"2010-07-07T10:34:10Z","abstract_excerpt":"The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\\vec{E}(\\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial differential equations of infinite order for the sixteen irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory (QKT) is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field $E(t)=E_0$ and the Sauter-type e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1099","kind":"arxiv","version":2},"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":"2026-05-18T04:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQrRolUmrGfhnzuUHuoC6yqxuhb0uDI/xS3oxeLV0JxNdKnUPcs8IihC91sx5avEfyA3pXuV6txpZZY74lR2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T11:17:01.922521Z"},"content_sha256":"01b90d59f560ef2fcec91834c38287c2e26f6b4cd13749a0de32b66d35858b21","schema_version":"1.0","event_id":"sha256:01b90d59f560ef2fcec91834c38287c2e26f6b4cd13749a0de32b66d35858b21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7CQMVDAOG4TVFHUKGZ6OGMVRUA/bundle.json","state_url":"https://pith.science/pith/7CQMVDAOG4TVFHUKGZ6OGMVRUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7CQMVDAOG4TVFHUKGZ6OGMVRUA/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":"2026-05-21T11:17:01Z","links":{"resolver":"https://pith.science/pith/7CQMVDAOG4TVFHUKGZ6OGMVRUA","bundle":"https://pith.science/pith/7CQMVDAOG4TVFHUKGZ6OGMVRUA/bundle.json","state":"https://pith.science/pith/7CQMVDAOG4TVFHUKGZ6OGMVRUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7CQMVDAOG4TVFHUKGZ6OGMVRUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7CQMVDAOG4TVFHUKGZ6OGMVRUA","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":"4e6a347cc5dfd1a0e235eaa76e9637d131cbe58bc376811eb7c2a07ba758f300","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-07-07T10:34:10Z","title_canon_sha256":"6a590919c67854cdc36cc49046c9cf2b4e9183195647cf6b509f0d114f9827b5"},"schema_version":"1.0","source":{"id":"1007.1099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1099","created_at":"2026-05-18T04:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1099v2","created_at":"2026-05-18T04:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1099","created_at":"2026-05-18T04:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"7CQMVDAOG4TV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7CQMVDAOG4TVFHUK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7CQMVDAO","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:01b90d59f560ef2fcec91834c38287c2e26f6b4cd13749a0de32b66d35858b21","target":"graph","created_at":"2026-05-18T04:32:46Z","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":"The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\\vec{E}(\\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial differential equations of infinite order for the sixteen irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory (QKT) is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field $E(t)=E_0$ and the Sauter-type e","authors_text":"Florian Hebenstreit, Holger Gies, Reinhard Alkofer","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-07-07T10:34:10Z","title":"Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1099","kind":"arxiv","version":2},"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:b5c14abc28cee98a4ad3e6468152d569920d992f2dc0592345777c37ff749db3","target":"record","created_at":"2026-05-18T04:32:46Z","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":"4e6a347cc5dfd1a0e235eaa76e9637d131cbe58bc376811eb7c2a07ba758f300","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-07-07T10:34:10Z","title_canon_sha256":"6a590919c67854cdc36cc49046c9cf2b4e9183195647cf6b509f0d114f9827b5"},"schema_version":"1.0","source":{"id":"1007.1099","kind":"arxiv","version":2}},"canonical_sha256":"f8a0ca8c0e3727529e8a367ce332b1a0223b1a49b4f0aef23faab881d4c35fce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8a0ca8c0e3727529e8a367ce332b1a0223b1a49b4f0aef23faab881d4c35fce","first_computed_at":"2026-05-18T04:32:46.208925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:46.208925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0wP4x7uuQeR9sXWvD+8JPSFn56oU6+hN2wyO7sUfjusJaupJNCupxHrzOvjcvnncOs/40G6sRf6MgpLQ+94VDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:46.209383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5c14abc28cee98a4ad3e6468152d569920d992f2dc0592345777c37ff749db3","sha256:01b90d59f560ef2fcec91834c38287c2e26f6b4cd13749a0de32b66d35858b21"],"state_sha256":"1f73a91fb3735e7f6c4a770c9d2184d099de44efcc2c0fd8c9f9ffd18f0390ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YIivHse0xPxZcffZuPcRD6sWEiZpuBrDlzxivvUo+1oH8x4YKvmsc+dt4/okUQOgAPDvxswclf8zP4hzPPPUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T11:17:01.925650Z","bundle_sha256":"9deb0dcd58c9e26c88168231025afbe6e8b01ecd96ddcfdb9fcd26573606c4ea"}}