{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SP6QI66MMU64VCQO2USSOTRAVY","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":"bb0f8c305ab1bb13d4ff3f43d1feea09389882afdbdd7d760519dc1345b88f57","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2016-09-15T17:33:22Z","title_canon_sha256":"785e19288b0bd331f2a52d5dcde4fdeaf324d8f372bbed5b2b3c23eb89169891"},"schema_version":"1.0","source":{"id":"1609.04749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04749","created_at":"2026-05-18T01:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04749v1","created_at":"2026-05-18T01:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04749","created_at":"2026-05-18T01:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"SP6QI66MMU64","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SP6QI66MMU64VCQO","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SP6QI66M","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:54f979bacb355e57c85855289103f1c7c6df797485c636d1be20c92fe56728c3","target":"graph","created_at":"2026-05-18T01:04:35Z","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":"The projective curvature tensor $P$ is invariant under a geodesic preserving transformation on a semi-Riemannian manifold. It is well known that $P$ is not a generalized curvature tensor and hence it possesses different geometric properties than other generalized curvature tensors. The main object of the present paper is to study some semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor. The reduced pseudosymmetric type structures for various Walker type conditions are deduced and the existence of Venzi space is ensured. It is","authors_text":"Absos Ali Shaikh, Haradhan Kundu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2016-09-15T17:33:22Z","title":"On some curvature restricted geometric structures for projective curvature tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04749","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":"sha256:430ed796da54c4e34dda6c800e6b4b3197a454fe60a80e8e91d08a152f0cbd72","target":"record","created_at":"2026-05-18T01:04:35Z","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":"bb0f8c305ab1bb13d4ff3f43d1feea09389882afdbdd7d760519dc1345b88f57","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2016-09-15T17:33:22Z","title_canon_sha256":"785e19288b0bd331f2a52d5dcde4fdeaf324d8f372bbed5b2b3c23eb89169891"},"schema_version":"1.0","source":{"id":"1609.04749","kind":"arxiv","version":1}},"canonical_sha256":"93fd047bcc653dca8a0ed525274e20ae06ffd49a13eab28168d96d8020b08eda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93fd047bcc653dca8a0ed525274e20ae06ffd49a13eab28168d96d8020b08eda","first_computed_at":"2026-05-18T01:04:35.676847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:35.676847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6PMzDAmpC1oNvG7r2lYQYBStx5JaOv1QFH8cXju+O5GZGd3HkMQ5wYQ4gA29FhMdaQJWodGtZznRutC4wGOLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:35.677626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:430ed796da54c4e34dda6c800e6b4b3197a454fe60a80e8e91d08a152f0cbd72","sha256:54f979bacb355e57c85855289103f1c7c6df797485c636d1be20c92fe56728c3"],"state_sha256":"e250e31896ef08ea0b44540c0414430582b1f390e6caa093ff75e18d529d778a"}