{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:75NSEHNR6GGFFCL4HNKCDGABI5","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":"3fdc4d70df331f43dea4643f3c8b28b4265fb98c9a26a95849172de113a87611","cross_cats_sorted":["gr-qc","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-07T14:16:41Z","title_canon_sha256":"3af1ab738a69bdce8b4c570c650923d60f393d6b4c14aa37ad56c7738b6e9090"},"schema_version":"1.0","source":{"id":"1002.1454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1454","created_at":"2026-05-18T02:09:18Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1454v1","created_at":"2026-05-18T02:09:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1454","created_at":"2026-05-18T02:09:18Z"},{"alias_kind":"pith_short_12","alias_value":"75NSEHNR6GGF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"75NSEHNR6GGFFCL4","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"75NSEHNR","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:19f55793a07624252de6e84e99828a335197521a7ff9ea673ac2d56428c5d54e","target":"graph","created_at":"2026-05-18T02:09:18Z","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 present, for both minkowskian and euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for minkowskian signature elliptic functions are essential in the metric while for euclidean signature only elementary functions appear.","authors_text":"Galliano Valent (LPTHE)","cross_cats":["gr-qc","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-07T14:16:41Z","title":"Bianchi type II,III and V diagonal Einstein metrics re-visited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1454","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:f2eb96c58122f111ca9d0ebb28fea4df7428a6d4cd6b3bf9a4993d7dde9e01c4","target":"record","created_at":"2026-05-18T02:09:18Z","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":"3fdc4d70df331f43dea4643f3c8b28b4265fb98c9a26a95849172de113a87611","cross_cats_sorted":["gr-qc","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-07T14:16:41Z","title_canon_sha256":"3af1ab738a69bdce8b4c570c650923d60f393d6b4c14aa37ad56c7738b6e9090"},"schema_version":"1.0","source":{"id":"1002.1454","kind":"arxiv","version":1}},"canonical_sha256":"ff5b221db1f18c52897c3b5421980147479eeda8c7614d16325b53855be35477","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff5b221db1f18c52897c3b5421980147479eeda8c7614d16325b53855be35477","first_computed_at":"2026-05-18T02:09:18.604791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:18.604791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ho79VyOy3eWb9mCgrKY6LYo4MD0ZGRF0v86R3ywK1Qtt7MBUCg/mJxWfulNm9X5kmxF90CoioV0lahRSGLTNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:18.605575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2eb96c58122f111ca9d0ebb28fea4df7428a6d4cd6b3bf9a4993d7dde9e01c4","sha256:19f55793a07624252de6e84e99828a335197521a7ff9ea673ac2d56428c5d54e"],"state_sha256":"7c8178fc7dae625b588608779abe503bd9b499deb765876471d90f0924c447ec"}