{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DRLUVMNENM2EFO32VAPBKSC5R6","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":"9ad01efcc9869aab7337ba95d08c875164d1567833e6034bd4b3e76e17504628","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-22T07:29:46Z","title_canon_sha256":"2898ee7e58ffc0fd4224e396fb4ca59204714aeffb3a06ffb41608f70e0fafce"},"schema_version":"1.0","source":{"id":"1512.06975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06975","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06975v1","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06975","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"pith_short_12","alias_value":"DRLUVMNENM2E","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DRLUVMNENM2EFO32","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DRLUVMNE","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:fff0105e8d044843ce9d98a4d1d7895a18f2628b156a1d371af0712aaf53e702","target":"graph","created_at":"2026-05-18T01:23:50Z","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 study proper curvature collineations in the most general form of the Bianchi types VI_{0} and VII_{0} space-times using the rank of the 6X6 Riemann matrix and direct integration technique. It is shown that when the above space-times admit proper curvature collineations, they form an infinite dimensional vector space.","authors_text":"Amjad Ali, Ghulam Shabbir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-22T07:29:46Z","title":"A note on proper curvature collineations in Bianchi types VI_{0} and VII_{0} space-times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06975","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":"sha256:0a9ed615a9c59dd8f9ec5dea040e77adc5a5f1217b34037ec4a79422db257b24","target":"record","created_at":"2026-05-18T01:23:50Z","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":"9ad01efcc9869aab7337ba95d08c875164d1567833e6034bd4b3e76e17504628","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-22T07:29:46Z","title_canon_sha256":"2898ee7e58ffc0fd4224e396fb4ca59204714aeffb3a06ffb41608f70e0fafce"},"schema_version":"1.0","source":{"id":"1512.06975","kind":"arxiv","version":1}},"canonical_sha256":"1c574ab1a46b3442bb7aa81e15485d8fbc0f13122587df7bf8d069528b59128f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c574ab1a46b3442bb7aa81e15485d8fbc0f13122587df7bf8d069528b59128f","first_computed_at":"2026-05-18T01:23:50.246155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:50.246155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RCO2h31RSl6BNuEoJ6dukWzSy5hR4RSGn7PfSxMSI6VWDiIdIKdlndBiojh7oFYZH9XWdEC2NsI67mbCn2MSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:50.246820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a9ed615a9c59dd8f9ec5dea040e77adc5a5f1217b34037ec4a79422db257b24","sha256:fff0105e8d044843ce9d98a4d1d7895a18f2628b156a1d371af0712aaf53e702"],"state_sha256":"09b24ff62c136ae35e0364cc78c9c7980304f4589d66b257e9f22d3a22da569e"}