{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GTSYNZBROYNTDM56JSHHS2Z7RC","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":"d4848d94977341bbcf35737697399c4b6e5fa6b2d966c0226012575ee170c6da","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-14T07:46:47Z","title_canon_sha256":"fa1ba001d23db1df598f14c353acafdb381d23176cb75b38d61f2587bee0941a"},"schema_version":"1.0","source":{"id":"1709.04644","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04644","created_at":"2026-05-18T00:24:42Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04644v2","created_at":"2026-05-18T00:24:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04644","created_at":"2026-05-18T00:24:42Z"},{"alias_kind":"pith_short_12","alias_value":"GTSYNZBROYNT","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GTSYNZBROYNTDM56","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GTSYNZBR","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:9fb384e930e6200efd936c5f7e7e6a5a0d1ce08d2815f6d8800bf233c108a39b","target":"graph","created_at":"2026-05-18T00:24:42Z","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":"We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a $(2+1)$-dimensional Minkowski (flat) space. For each of the sets we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.","authors_text":"A.I. Breev, A.V. Shapovalov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-14T07:46:47Z","title":"Symmetry operators and separation of variables in the $(2+1)$-dimensional Dirac equation with external electromagnetic field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04644","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":"sha256:056969999d9d18a6593360b1f21a6491186de48d5a0b49524678e601d6a1f368","target":"record","created_at":"2026-05-18T00:24:42Z","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":"d4848d94977341bbcf35737697399c4b6e5fa6b2d966c0226012575ee170c6da","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-14T07:46:47Z","title_canon_sha256":"fa1ba001d23db1df598f14c353acafdb381d23176cb75b38d61f2587bee0941a"},"schema_version":"1.0","source":{"id":"1709.04644","kind":"arxiv","version":2}},"canonical_sha256":"34e586e431761b31b3be4c8e796b3f888e57102b3768b2ff67fadde3334bfa0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34e586e431761b31b3be4c8e796b3f888e57102b3768b2ff67fadde3334bfa0c","first_computed_at":"2026-05-18T00:24:42.466599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:42.466599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s9Ux6dXXO8QH2mranjt/VuTOKwhVOTaIa/kdcnuBlbB5ZEGQ7SSeDpjyLWDFZIclYSvprkgReFTdQaJ7slJUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:42.467231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04644","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:056969999d9d18a6593360b1f21a6491186de48d5a0b49524678e601d6a1f368","sha256:9fb384e930e6200efd936c5f7e7e6a5a0d1ce08d2815f6d8800bf233c108a39b"],"state_sha256":"c7c1375270a95a68878c8d63dd45cbf5bee1d7d8efffc6e6b81469fefcd8cccf"}