{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5IGT4TILMYKCYQZDXVOGMH3LGJ","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":"8745d2a463ff7eefb7d065945a2de3a585d3a520b33e08d09058f57aa3617cfd","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-11-13T15:27:18Z","title_canon_sha256":"af4748255f4c72ae649f68c662233027b8c8ee87008a55ad5f94f422b9e5c44e"},"schema_version":"1.0","source":{"id":"1611.04143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04143","created_at":"2026-05-18T00:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04143v1","created_at":"2026-05-18T00:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04143","created_at":"2026-05-18T00:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"5IGT4TILMYKC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5IGT4TILMYKCYQZD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5IGT4TIL","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:a0626df733fefe3a292a5e6a805c35ec1a0d7315a29b5231115b0a9eae960560","target":"graph","created_at":"2026-05-18T00:51:42Z","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":"In (3 + 1) spacetime dimensions the Rainich conditions are a set of equations expressed solely in terms of the metric tensor which are equivalent to the Einstein-Maxwell equations for non-null electromagnetic fields. Here we provide the analogous conditions for (2 + 1)-dimensional gravity coupled to electromagnetism. Both the non-null and null cases are treated. The construction of these conditions is based upon reducing the problem to that of gravity coupled to a scalar field, which we have treated elsewhere. These conditions can be easily extended to other theories of (2 + 1)-dimensional gra","authors_text":"C. G. Torre, D. S. Krongos","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-11-13T15:27:18Z","title":"Rainich Conditions in (2+1)-Dimensional Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04143","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":"sha256:685988f6f2a53e9162c5013f78e73a2a744e9518c0e0dc246e23176d3779b156","target":"record","created_at":"2026-05-18T00:51:42Z","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":"8745d2a463ff7eefb7d065945a2de3a585d3a520b33e08d09058f57aa3617cfd","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-11-13T15:27:18Z","title_canon_sha256":"af4748255f4c72ae649f68c662233027b8c8ee87008a55ad5f94f422b9e5c44e"},"schema_version":"1.0","source":{"id":"1611.04143","kind":"arxiv","version":1}},"canonical_sha256":"ea0d3e4d0b66142c4323bd5c661f6b327789ba8698e53276c725320baedf6561","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea0d3e4d0b66142c4323bd5c661f6b327789ba8698e53276c725320baedf6561","first_computed_at":"2026-05-18T00:51:42.400370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:42.400370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aCjLiN5F8b14+H+YY2SLhfPF/YLuS06Knf8AS1wGTlPYXx7L6p2saZmoDTPsMFnypiPMoHPAEyVQkwtPN2iHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:42.401000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:685988f6f2a53e9162c5013f78e73a2a744e9518c0e0dc246e23176d3779b156","sha256:a0626df733fefe3a292a5e6a805c35ec1a0d7315a29b5231115b0a9eae960560"],"state_sha256":"797bcc34af079294ccaeb69e1254b0919602e056632ede1c00f192decb40f1ac"}