{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:COY5OA7V3WM42X4XZZT3AALIIS","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":"3aaa9fe46d7894504bad0cabb7ba1c0458e9028546a738e6b25b8914d6200cdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-16T05:44:43Z","title_canon_sha256":"28d754f0c675bda03aef2828d4b22f4730930b6dfc5fd70bbb0c6336c520ad98"},"schema_version":"1.0","source":{"id":"1006.3132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3132","created_at":"2026-05-18T01:09:23Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3132v1","created_at":"2026-05-18T01:09:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3132","created_at":"2026-05-18T01:09:23Z"},{"alias_kind":"pith_short_12","alias_value":"COY5OA7V3WM4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"COY5OA7V3WM42X4X","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"COY5OA7V","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:91a15aa267169c31c30fc4bbc35e681f145e2a9759ff0c502248fbcfddcca51d","target":"graph","created_at":"2026-05-18T01:09:23Z","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 Eisenhart problem of finding parallel tensors is solved for the symmetric case in the regular $f$-Kenmotsu framework. On this way, the Olszack-Rosca example of Einstein manifolds provided by $f$-Kenmotsu manifolds via locally symmetric Ricci tensors is recovered as well as a case of Killing vector fields. Some other classes of Einstein-Kenmotsu manifolds are presented. Our result is interpreted in terms of Ricci solitons and special quadratic first integrals.","authors_text":"Constantin C\\u{a}lin, Mircea Crasmareanu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-16T05:44:43Z","title":"From the Eisenhart problem to Ricci solitons in $f$-Kenmotsu manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3132","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:d37dfa7ba9b59af016331a6cdc04a9dbb716d73dcf471b5580e13c278e2d1518","target":"record","created_at":"2026-05-18T01:09:23Z","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":"3aaa9fe46d7894504bad0cabb7ba1c0458e9028546a738e6b25b8914d6200cdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-16T05:44:43Z","title_canon_sha256":"28d754f0c675bda03aef2828d4b22f4730930b6dfc5fd70bbb0c6336c520ad98"},"schema_version":"1.0","source":{"id":"1006.3132","kind":"arxiv","version":1}},"canonical_sha256":"13b1d703f5dd99cd5f97ce67b00168448f0688c264bb07e3a4da72a9848f8192","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13b1d703f5dd99cd5f97ce67b00168448f0688c264bb07e3a4da72a9848f8192","first_computed_at":"2026-05-18T01:09:23.885992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:23.885992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1lUeHYX+k1TR18PARnuvi2bh6cg0IDo32SKAxffDEloJSP6lhIo/IdcR/MDUFy1309DBcO+cL4tWcSQ2mp23DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:23.886583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d37dfa7ba9b59af016331a6cdc04a9dbb716d73dcf471b5580e13c278e2d1518","sha256:91a15aa267169c31c30fc4bbc35e681f145e2a9759ff0c502248fbcfddcca51d"],"state_sha256":"b5540c44d1435f577066355aee6edca0591487f3167f5f8758fa360e25c3b789"}