{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ICYPRWTVO7YD6E4XQ6BTBWZGKX","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":"670f8800ac777d369793d708f1d4788017e75d7de7fa635ced0124181e6e56cd","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-03-25T21:12:13Z","title_canon_sha256":"6f356a99431eb8ad32a3b4c09d2116545d18f97d8fa9c949bdec5a5afd15b853"},"schema_version":"1.0","source":{"id":"1403.6511","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6511","created_at":"2026-05-18T01:43:51Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6511v2","created_at":"2026-05-18T01:43:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6511","created_at":"2026-05-18T01:43:51Z"},{"alias_kind":"pith_short_12","alias_value":"ICYPRWTVO7YD","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ICYPRWTVO7YD6E4X","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ICYPRWTV","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:a4fd6a2314c122913f3e8d7aa055a91f11132fc127363ac9c00b9e9c5c0809e2","target":"graph","created_at":"2026-05-18T01:43:51Z","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":"Geroch's solution-generating method is extended to the case of Einstein spaces, which possess a Killing vector {{}and are thus asymptotically (locally) (anti-)de Sitter}. This includes the reduction to a three-dimensional coset space, the description of the dynamics in terms of a sigma-model and its transformation properties under the $SL(2,\\mathbb{R})$ group, and the reconstruction of new four-dimensional Einstein spaces. The detailed analysis of the space of solutions is performed using the Hamilton--Jacobi method in the instance where the three-dimensional coset space is conformal to $\\math","authors_text":"Anastasios C. Petkou (Aristotle U. Thessaloniki), Chennai), CPHT), (Illinois U. Urbana), P. Marios Petropoulos (Ecole Polytechnique, Prasanta K. Tripathy (Indian Institute of Technology, Robert G. Leigh","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-03-25T21:12:13Z","title":"The Geroch group in Einstein spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6511","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":"sha256:22fbd13a2dc8003bfb9a36f9664613622b9d6d26908b04218e26d87e13de3e98","target":"record","created_at":"2026-05-18T01:43:51Z","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":"670f8800ac777d369793d708f1d4788017e75d7de7fa635ced0124181e6e56cd","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-03-25T21:12:13Z","title_canon_sha256":"6f356a99431eb8ad32a3b4c09d2116545d18f97d8fa9c949bdec5a5afd15b853"},"schema_version":"1.0","source":{"id":"1403.6511","kind":"arxiv","version":2}},"canonical_sha256":"40b0f8da7577f03f1397878330db2655c2011e5b9533c9027d25e0f0cf2f8a0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40b0f8da7577f03f1397878330db2655c2011e5b9533c9027d25e0f0cf2f8a0d","first_computed_at":"2026-05-18T01:43:51.197606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:51.197606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bbwUU7o2SklUMlHDccFe4JnzHFK20tiJlZP3YtqPcDe5CL1d/vG2AgRtn7i1fXZsvitkCo0UJJ+FqxbjdQZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:51.198178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6511","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22fbd13a2dc8003bfb9a36f9664613622b9d6d26908b04218e26d87e13de3e98","sha256:a4fd6a2314c122913f3e8d7aa055a91f11132fc127363ac9c00b9e9c5c0809e2"],"state_sha256":"865f43301a3cf3459c64eabcad030cd0813df2d87386b318da88df0eb912f2eb"}