{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Y4YLGP2VP5SP4WUYI6SJBH7TYE","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":"00ea7611a9b1272bb568ba498e196d6f3ff083556d783482538ddebd02afb20e","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-02-10T16:08:35Z","title_canon_sha256":"4d474164bbf281ae47a7dba0718c7330ed0a25115e5e59ce2d507e42d8a48c3f"},"schema_version":"1.0","source":{"id":"0902.1685","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1685","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1685v2","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1685","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"Y4YLGP2VP5SP","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Y4YLGP2VP5SP4WUY","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Y4YLGP2V","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:9ca6ac9092002226fb7a3e33697f87536bb59c9427c42eb27e1d43f96cb57741","target":"graph","created_at":"2026-05-18T02:14:48Z","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 prove involutivity of Einstein, Einstein-Maxwell and other field equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kahler theory are derived.","authors_text":"Boris Kruglikov","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-02-10T16:08:35Z","title":"Involutivity of field equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1685","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":"sha256:65dfe94e255f0cef45e3b3234e5395c3c74db3598d5ffdd733056481992466be","target":"record","created_at":"2026-05-18T02:14:48Z","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":"00ea7611a9b1272bb568ba498e196d6f3ff083556d783482538ddebd02afb20e","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-02-10T16:08:35Z","title_canon_sha256":"4d474164bbf281ae47a7dba0718c7330ed0a25115e5e59ce2d507e42d8a48c3f"},"schema_version":"1.0","source":{"id":"0902.1685","kind":"arxiv","version":2}},"canonical_sha256":"c730b33f557f64fe5a9847a4909ff3c13d074cd96f4c3866cc590c2d80a41551","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c730b33f557f64fe5a9847a4909ff3c13d074cd96f4c3866cc590c2d80a41551","first_computed_at":"2026-05-18T02:14:48.482471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:48.482471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ZbsYahcDeMceoNpemJN/3vAhn5PN3y5B0+31kb5V24NWou+7Udw22KcKRVSb4YsB3pPHJBJ4+t3ruuRtBDmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:48.483086Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.1685","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65dfe94e255f0cef45e3b3234e5395c3c74db3598d5ffdd733056481992466be","sha256:9ca6ac9092002226fb7a3e33697f87536bb59c9427c42eb27e1d43f96cb57741"],"state_sha256":"b7e749e699218536e7f83e1e0132670c42971b0581b0c048f6cf4a1715eb4f4f"}