{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5AF3Y5NMJL6EO6VJLTBJQ3NTET","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":"2e98b0572952bae4415a0ae5cbc65dacd00c018d742533fffe44fca099b75b39","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-09-19T20:39:49Z","title_canon_sha256":"69725fe350af720042fcef01d0c0789dfbc6fd170ae40217343cd30e2b084516"},"schema_version":"1.0","source":{"id":"1909.09229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.09229","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"1909.09229v2","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.09229","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"5AF3Y5NMJL6E","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"pith_short_16","alias_value":"5AF3Y5NMJL6EO6VJ","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"pith_short_8","alias_value":"5AF3Y5NM","created_at":"2026-07-05T01:59:09Z"}],"graph_snapshots":[{"event_id":"sha256:c5f53da4ed3459530635c86a482fdda62b927f15d93c9bfef96dab50d9f8f02e","target":"graph","created_at":"2026-07-05T01:59:09Z","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/1909.09229/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski space. After a brief recap of the Dirac equation and its solution space, in order to allow for the effects of a possibly nonstandard structure of spacetime at the Planck scale, a regularization by a smooth cutoff in momentum space is introduced, and its properties are discussed. Given an ensemble of solutions, we recall the construction of a local correlation function, which realizes spacetime in terms of operators. It is shown in various situations that the ","authors_text":"Marco Oppio","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-09-19T20:39:49Z","title":"On the Mathematical Foundations of Causal Fermion Systems in Minkowski Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.09229","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":"sha256:495ece120411015420f27c65db08d49252104a199e56165da4dbccff50ad269c","target":"record","created_at":"2026-07-05T01:59:09Z","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":"2e98b0572952bae4415a0ae5cbc65dacd00c018d742533fffe44fca099b75b39","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-09-19T20:39:49Z","title_canon_sha256":"69725fe350af720042fcef01d0c0789dfbc6fd170ae40217343cd30e2b084516"},"schema_version":"1.0","source":{"id":"1909.09229","kind":"arxiv","version":2}},"canonical_sha256":"e80bbc75ac4afc477aa95cc2986db324f9f471fc7c55ecb5f121d100bbc8d82a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e80bbc75ac4afc477aa95cc2986db324f9f471fc7c55ecb5f121d100bbc8d82a","first_computed_at":"2026-07-05T01:59:09.605033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:59:09.605033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kegUHuIpyAy7LC4BnE3oOoS4nVr4guNqrG1ZDeCSz2Q1zEgkVQBtCpHgY49zKhIiC2SdUGCJaLxM+pOOS2DRBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:59:09.605472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.09229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:495ece120411015420f27c65db08d49252104a199e56165da4dbccff50ad269c","sha256:c5f53da4ed3459530635c86a482fdda62b927f15d93c9bfef96dab50d9f8f02e"],"state_sha256":"8455e7d1ba9d85bbd79ac47327261605cfeaf45a697e395a83e89d6165d6120b"}