{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MLGTVWSD7LNJ23XX7WP3K77W3W","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":"77dbfb9ef820daf78a8adc7e223645ebb1f89572052b96a967439eab760f4d75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-04-02T16:36:19Z","title_canon_sha256":"d1d5ad0d5ff9c926ef7ee83d23adfd3a49568f8864de9049c727a0899e62d6e0"},"schema_version":"1.0","source":{"id":"0904.0423","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.0423","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"arxiv_version","alias_value":"0904.0423v2","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0423","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"pith_short_12","alias_value":"MLGTVWSD7LNJ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MLGTVWSD7LNJ23XX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MLGTVWSD","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:c1ab15fc0f6351bbc4d79abba314bce5a657f13c1d10adb74ee11cc24aac06eb","target":"graph","created_at":"2026-05-18T04:27:28Z","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 give a pedagogical introduction into an old, but unfortunately not commonly known formulation of GR in terms of self-dual two-forms due to in particular Jerzy Plebanski. Our presentation is rather explicit in that we show how the familiar textbook solutions: Schwarzschild, Volkoff-Oppenheimer, as well as those describing the Newtonian limit, a gravitational wave and the homogeneous isotropic Universe can be obtained within this formalism. Our description shows how Plebanski formulation gives quite an economical alternative to the usual metric and frame-based schemes for deriving Einstein eq","authors_text":"Kirill Krasnov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-04-02T16:36:19Z","title":"Plebanski Formulation of General Relativity: A Practical Introduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0423","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:b6ec33d43723fa45ffad5834830ce700babb1a3174ad78888c46dd4e0eb1f3a6","target":"record","created_at":"2026-05-18T04:27:28Z","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":"77dbfb9ef820daf78a8adc7e223645ebb1f89572052b96a967439eab760f4d75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-04-02T16:36:19Z","title_canon_sha256":"d1d5ad0d5ff9c926ef7ee83d23adfd3a49568f8864de9049c727a0899e62d6e0"},"schema_version":"1.0","source":{"id":"0904.0423","kind":"arxiv","version":2}},"canonical_sha256":"62cd3ada43fada9d6ef7fd9fb57ff6dda7b01049b4cd9b2c8f66c3f6d644cc00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62cd3ada43fada9d6ef7fd9fb57ff6dda7b01049b4cd9b2c8f66c3f6d644cc00","first_computed_at":"2026-05-18T04:27:28.371676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:28.371676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9C7mA2C7k2oxGNSMrI2yIReQCl1toouRy+JRc/lL4mcYfo7S4+K0bXG9vtpWRvpiT07ZaSUPquhGPQrtTZXRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:28.372080Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.0423","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6ec33d43723fa45ffad5834830ce700babb1a3174ad78888c46dd4e0eb1f3a6","sha256:c1ab15fc0f6351bbc4d79abba314bce5a657f13c1d10adb74ee11cc24aac06eb"],"state_sha256":"ab92413e456ece21c1a15e964976c4ae6175db7333524e4cfffda956125eb24a"}