{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UX7RANY7KSTIXOXWNT5AUVSTEX","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":"63ed42289380af65613752856d2c4b3f35426e8b2d06b61e72d70746134206ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-28T07:26:16Z","title_canon_sha256":"23ba2fc3e411957c72447dca35b867bab362b44c1f1d5fd3c35160f8491ab3cc"},"schema_version":"1.0","source":{"id":"1202.6138","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6138","created_at":"2026-05-18T04:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6138v1","created_at":"2026-05-18T04:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6138","created_at":"2026-05-18T04:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"UX7RANY7KSTI","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UX7RANY7KSTIXOXW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UX7RANY7","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:d3b380eb4bc881eea854b6e20c66a609c2012e1b6f6eb4c8233fbe712fa5c661","target":"graph","created_at":"2026-05-18T04:01:14Z","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":"$(N(k),\\xi)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),\\xi)$-semi-Riemannian manifolds are given. Some relations involving ${\\cal T}_{a}$-curvature tensor in $(N(k),\\xi)$-semi-Riemannian manifolds are proved. $\\xi $-${\\cal T}_{a}$-flat $(N(k),\\xi)$-semi-Riemannian manifolds are defined. It is proved that if $M$ is an $n$-dimensional $\\xi $-${\\cal T}_{a}$-flat $(N(k),\\xi)$-semi-Riemannian manifold, then it is $\\eta $-Einstein under an algebraic condition. We prove that a semi-Riemannian manifold, which is $T$-recurrent or $T$-symmetric, is always $T$-semisymmetric","authors_text":"Mukut Mani Tripathi, Punam Gupta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-28T07:26:16Z","title":"On $(N(k),\\xi)$-semi-Riemannian manifolds: Semisymmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6138","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:bc1be66121c4aec27bea7fb4891faadbb2d65f92fe94a25e02c0c80695a9ee79","target":"record","created_at":"2026-05-18T04:01:14Z","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":"63ed42289380af65613752856d2c4b3f35426e8b2d06b61e72d70746134206ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-28T07:26:16Z","title_canon_sha256":"23ba2fc3e411957c72447dca35b867bab362b44c1f1d5fd3c35160f8491ab3cc"},"schema_version":"1.0","source":{"id":"1202.6138","kind":"arxiv","version":1}},"canonical_sha256":"a5ff10371f54a68bbaf66cfa0a565325d0ecaec38eaa7ea8500959b0d4a3c21d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5ff10371f54a68bbaf66cfa0a565325d0ecaec38eaa7ea8500959b0d4a3c21d","first_computed_at":"2026-05-18T04:01:14.121988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:14.121988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hrk4EqUAXAOhc6RShtGzek8xY/GrnwFo1aXQaPPChe4NFFlthyUtOOdapFJ1caYI2tmjlPC32WdLYaNII7oSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:14.122417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6138","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc1be66121c4aec27bea7fb4891faadbb2d65f92fe94a25e02c0c80695a9ee79","sha256:d3b380eb4bc881eea854b6e20c66a609c2012e1b6f6eb4c8233fbe712fa5c661"],"state_sha256":"c3fa966ac8df628ad79d9c2bbdc80aba065b93f272eea9035c77f597338e98e5"}