{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TDCIELKZRIJG7QJ7SD4MKXUVIK","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":"986702c95350012c966ab36561c7c2df1b92ff7493680236ae211fcc6209fba3","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-07T10:17:37Z","title_canon_sha256":"bb32d12e7a02bf5c219489aeb8c5ecb05c068c7b60500ad5be9f4bd0e47420bb"},"schema_version":"1.0","source":{"id":"1110.1475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1475","created_at":"2026-05-18T04:11:30Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1475v1","created_at":"2026-05-18T04:11:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1475","created_at":"2026-05-18T04:11:30Z"},{"alias_kind":"pith_short_12","alias_value":"TDCIELKZRIJG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TDCIELKZRIJG7QJ7","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TDCIELKZ","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:7c8bf9c352ec02d21c8b97cee96ca5b2f68b034b4d0cc2b28fced0ec001dcd81","target":"graph","created_at":"2026-05-18T04:11:30Z","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":"We survey the correct definition of a generalized Dirac operator on a Space--Time and the classical result about propagation of singularities. This says that light travels along light--like geodesics. Finally we show this is also true for generalized Dirac operators.","authors_text":"Paolo Antonini","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-07T10:17:37Z","title":"Generalized Dirac operators on Lorentzian manifolds and propagation of singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1475","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":"sha256:7db48431de6e789010cbc0ce0d0ab52f62adf591d3b8ae63a0e653b0ee905bcd","target":"record","created_at":"2026-05-18T04:11:30Z","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":"986702c95350012c966ab36561c7c2df1b92ff7493680236ae211fcc6209fba3","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-07T10:17:37Z","title_canon_sha256":"bb32d12e7a02bf5c219489aeb8c5ecb05c068c7b60500ad5be9f4bd0e47420bb"},"schema_version":"1.0","source":{"id":"1110.1475","kind":"arxiv","version":1}},"canonical_sha256":"98c4822d598a126fc13f90f8c55e9542af6e99bc9f7d2ec6ee16d1ce16b31701","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98c4822d598a126fc13f90f8c55e9542af6e99bc9f7d2ec6ee16d1ce16b31701","first_computed_at":"2026-05-18T04:11:30.011467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:30.011467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VAS2aJDTj8+Hbmx78tcKLqxl+qyAVxHmftUvbNpuAx+4TJhfr/xSnd5TP06E7SKeIpPhIYRoDiKKlrEbhU3mBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:30.012178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7db48431de6e789010cbc0ce0d0ab52f62adf591d3b8ae63a0e653b0ee905bcd","sha256:7c8bf9c352ec02d21c8b97cee96ca5b2f68b034b4d0cc2b28fced0ec001dcd81"],"state_sha256":"5e928a93d6a0ff6c4699ec345e1324791aead23cd77dd23cbf31a2ca5d483d73"}