{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WOUMKQ7QXTYVYHCUZTFGI2QBOP","short_pith_number":"pith:WOUMKQ7Q","canonical_record":{"source":{"id":"1111.4115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-17T14:49:26Z","cross_cats_sorted":["nucl-th","quant-ph"],"title_canon_sha256":"b65ec715626964e474031bc02279447fd5e8e1a6496c848d002195401c1d314e","abstract_canon_sha256":"8df700c9016661e395b250d79971c1df0984c329adae33a2a865e7c5e53c03bc"},"schema_version":"1.0"},"canonical_sha256":"b3a8c543f0bcf15c1c54ccca646a0173f75882f174314bce713a55ce2f373808","source":{"kind":"arxiv","id":"1111.4115","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4115","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4115v1","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4115","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"WOUMKQ7QXTYV","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WOUMKQ7QXTYVYHCU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WOUMKQ7Q","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WOUMKQ7QXTYVYHCUZTFGI2QBOP","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-17T14:49:26Z","cross_cats_sorted":["nucl-th","quant-ph"],"title_canon_sha256":"b65ec715626964e474031bc02279447fd5e8e1a6496c848d002195401c1d314e","abstract_canon_sha256":"8df700c9016661e395b250d79971c1df0984c329adae33a2a865e7c5e53c03bc"},"schema_version":"1.0"},"canonical_sha256":"b3a8c543f0bcf15c1c54ccca646a0173f75882f174314bce713a55ce2f373808","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:05.657296Z","signature_b64":"HrByubAqoKIFCyt2WIFYQcQMHwprwqEUM5eO/sdC0PFI6K/3T1hy/+SKXiS9cZxMlsMzKGFcOd5VAVEsM8ysAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3a8c543f0bcf15c1c54ccca646a0173f75882f174314bce713a55ce2f373808","last_reissued_at":"2026-05-18T04:08:05.656840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:05.656840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4115","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":"2026-05-18T04:08:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0VVf9JEKz/4yMW1rCsOLIP+bIjhVsQOkxwRGDOe01A8G2TDeuUo7lLkJjZTlt2gYeDI9of59n+Yw28rwPoGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:51:58.139639Z"},"content_sha256":"d9e3ccc27ecbbcd10495930357186bf1c928cf0c67f18afa9146970efd0c27e6","schema_version":"1.0","event_id":"sha256:d9e3ccc27ecbbcd10495930357186bf1c928cf0c67f18afa9146970efd0c27e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WOUMKQ7QXTYVYHCUZTFGI2QBOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum field theory from classical statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th","quant-ph"],"primary_cat":"hep-th","authors_text":"C.Wetterich","submitted_at":"2011-11-17T14:49:26Z","abstract_excerpt":"An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4115","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":""},"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":"2026-05-18T04:08:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uVQHCAelWR4YRx2oCs9om9yWyNT3r1B/B8DziG782/kNdgYfUtM+1C8iMQekpwBTp5TtId3r1xeFu6HzN6oRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:51:58.140308Z"},"content_sha256":"6e8b1fafec0c10603071cf68919db939f37fd3cae61f744b498acf96abefbafc","schema_version":"1.0","event_id":"sha256:6e8b1fafec0c10603071cf68919db939f37fd3cae61f744b498acf96abefbafc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WOUMKQ7QXTYVYHCUZTFGI2QBOP/bundle.json","state_url":"https://pith.science/pith/WOUMKQ7QXTYVYHCUZTFGI2QBOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WOUMKQ7QXTYVYHCUZTFGI2QBOP/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":"2026-05-27T08:51:58Z","links":{"resolver":"https://pith.science/pith/WOUMKQ7QXTYVYHCUZTFGI2QBOP","bundle":"https://pith.science/pith/WOUMKQ7QXTYVYHCUZTFGI2QBOP/bundle.json","state":"https://pith.science/pith/WOUMKQ7QXTYVYHCUZTFGI2QBOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WOUMKQ7QXTYVYHCUZTFGI2QBOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WOUMKQ7QXTYVYHCUZTFGI2QBOP","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":"8df700c9016661e395b250d79971c1df0984c329adae33a2a865e7c5e53c03bc","cross_cats_sorted":["nucl-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-17T14:49:26Z","title_canon_sha256":"b65ec715626964e474031bc02279447fd5e8e1a6496c848d002195401c1d314e"},"schema_version":"1.0","source":{"id":"1111.4115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4115","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4115v1","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4115","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"WOUMKQ7QXTYV","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WOUMKQ7QXTYVYHCU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WOUMKQ7Q","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:6e8b1fafec0c10603071cf68919db939f37fd3cae61f744b498acf96abefbafc","target":"graph","created_at":"2026-05-18T04:08:05Z","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":"An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic appro","authors_text":"C.Wetterich","cross_cats":["nucl-th","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-17T14:49:26Z","title":"Quantum field theory from classical statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4115","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:d9e3ccc27ecbbcd10495930357186bf1c928cf0c67f18afa9146970efd0c27e6","target":"record","created_at":"2026-05-18T04:08:05Z","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":"8df700c9016661e395b250d79971c1df0984c329adae33a2a865e7c5e53c03bc","cross_cats_sorted":["nucl-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-17T14:49:26Z","title_canon_sha256":"b65ec715626964e474031bc02279447fd5e8e1a6496c848d002195401c1d314e"},"schema_version":"1.0","source":{"id":"1111.4115","kind":"arxiv","version":1}},"canonical_sha256":"b3a8c543f0bcf15c1c54ccca646a0173f75882f174314bce713a55ce2f373808","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3a8c543f0bcf15c1c54ccca646a0173f75882f174314bce713a55ce2f373808","first_computed_at":"2026-05-18T04:08:05.656840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:05.656840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HrByubAqoKIFCyt2WIFYQcQMHwprwqEUM5eO/sdC0PFI6K/3T1hy/+SKXiS9cZxMlsMzKGFcOd5VAVEsM8ysAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:05.657296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9e3ccc27ecbbcd10495930357186bf1c928cf0c67f18afa9146970efd0c27e6","sha256:6e8b1fafec0c10603071cf68919db939f37fd3cae61f744b498acf96abefbafc"],"state_sha256":"4d044beec069d060f5388d5cea9f455b203da9ca01f15c025994b7a2381af29d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"71tM7J++p1r6uPnun9EH0a3xM4q2XguLhxjldk19hxHlpviLJ4B2XbBiLeoWLD9IDA4PqV3DE6eoiH7+sk9IDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:51:58.144009Z","bundle_sha256":"674118d655c4c50ee5f3fe3d3c2a7f58f10f479d0614d0550ee1efdf573c8856"}}