{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YZZ6PYYOWMPUCLUQRB34VD32HY","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":"02ab48492b99dc76775f54d4a0bd2d8c82d2b12febb6c375b85a541a3f5c9b14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-03T09:13:49Z","title_canon_sha256":"e22e239f5c58dc7ecce7bab88c7f930771706fd750e6779f309367b541d1e06d"},"schema_version":"1.0","source":{"id":"1506.03476","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03476","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03476v2","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03476","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"YZZ6PYYOWMPU","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YZZ6PYYOWMPUCLUQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YZZ6PYYO","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:f5e6a0820e395baa93871b94ef7c515ba1a6e7535749883fa8a3dde314720403","target":"graph","created_at":"2026-05-18T01:19:53Z","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":"In the differential geometry of certain F-structures, the role of W-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing W-tensor have been considered and the existence of Killing and conformal Killing vector fields has been established. Perfect fluid spacetimes with vanishing W-tensor have also been considered. The divergence of W-tensor is studied in detail and it is seen, among other results, that a perfect fluid spacetime with conserved W-tensor represents","authors_text":"Musavvir Ali, Zafar Ahsan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-03T09:13:49Z","title":"Curvature Tensor for the Spacetime of General Relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03476","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":"sha256:6d18d212dee34c5fe5fa3dee9f459d55c9cf57049f7c458551aa3040bd69ca36","target":"record","created_at":"2026-05-18T01:19:53Z","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":"02ab48492b99dc76775f54d4a0bd2d8c82d2b12febb6c375b85a541a3f5c9b14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-03T09:13:49Z","title_canon_sha256":"e22e239f5c58dc7ecce7bab88c7f930771706fd750e6779f309367b541d1e06d"},"schema_version":"1.0","source":{"id":"1506.03476","kind":"arxiv","version":2}},"canonical_sha256":"c673e7e30eb31f412e908877ca8f7a3e2b40a2f747305ef779ca899258eeb1dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c673e7e30eb31f412e908877ca8f7a3e2b40a2f747305ef779ca899258eeb1dc","first_computed_at":"2026-05-18T01:19:53.817763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:53.817763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"909HDi+cFi7TwUIRjTdO0WGhACmLxHtsO+FR78BAQfZ4HmDpioPWW4Ib4YAsUo3iGwgJv3h/yIqeEM+uAZrLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:53.818197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03476","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d18d212dee34c5fe5fa3dee9f459d55c9cf57049f7c458551aa3040bd69ca36","sha256:f5e6a0820e395baa93871b94ef7c515ba1a6e7535749883fa8a3dde314720403"],"state_sha256":"11988740451ca6934b13132d85ecd445fbac667a9ce70998fba93369dc1cd83c"}