{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TQCYJHTUBBFIG5PDLQC74PMIA4","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":"bd632e5fcf0bae91fc473ac9bdc2dca016ef12dcbc9c153a56dd6eafe5410ef8","cross_cats_sorted":["hep-th","math.DG","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T20:04:03Z","title_canon_sha256":"99b4097d36f38fa86ae13571a204d9634bf777ccb6585d601014ad28bb778baf"},"schema_version":"1.0","source":{"id":"1812.00038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00038","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00038v1","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00038","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"TQCYJHTUBBFI","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TQCYJHTUBBFIG5PD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TQCYJHTU","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:66cb2c76706084b1b327c8211b44a9ec25ac609f686dec6227b94f3cf1eeb9f9","target":"graph","created_at":"2026-05-17T23:59:27Z","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 subject of this PhD thesis is noncommutative geometry - more specifically spectral triples - and how it can be generalized to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis will thus be dedicated to the transition from Riemannian to semi-Riemannian manifolds. This entails a study of Clifford algebras for indefinite vector spaces and Spin structures on semi-Riemannian manifolds. An important consequence of this is the introduction of Krein spaces, which will enable us to generalize spectral triples to indefinite spectral triples. I","authors_text":"Nadir Bizi","cross_cats":["hep-th","math.DG","math.MP","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T20:04:03Z","title":"Thesis: Semi-Riemannian Noncommutative Geometry, Gauge Theory, and the Standard Model of Particle Physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00038","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:cc72195f50022c06ba1a31376bf5f19d0552997c7e07a2d5052126b83c178c5d","target":"record","created_at":"2026-05-17T23:59:27Z","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":"bd632e5fcf0bae91fc473ac9bdc2dca016ef12dcbc9c153a56dd6eafe5410ef8","cross_cats_sorted":["hep-th","math.DG","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T20:04:03Z","title_canon_sha256":"99b4097d36f38fa86ae13571a204d9634bf777ccb6585d601014ad28bb778baf"},"schema_version":"1.0","source":{"id":"1812.00038","kind":"arxiv","version":1}},"canonical_sha256":"9c05849e74084a8375e35c05fe3d8807342899ebbdb0e754fd9df151b9eaf6d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c05849e74084a8375e35c05fe3d8807342899ebbdb0e754fd9df151b9eaf6d3","first_computed_at":"2026-05-17T23:59:27.497343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:27.497343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y4sObq+wiGs+K6zNBire8D1gta3WOM+w1WQd71MlM+tv0YvILd8PCpYibqaoxCu6au8UuVTozpzh5se6hvaLBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:27.497807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc72195f50022c06ba1a31376bf5f19d0552997c7e07a2d5052126b83c178c5d","sha256:66cb2c76706084b1b327c8211b44a9ec25ac609f686dec6227b94f3cf1eeb9f9"],"state_sha256":"129ae5d357db27f7d102d10993318cf00950afdaab5d3d626b2f9d43d63d8b2d"}