{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CF3QSD6IUGL6RLNR6SNIH6YWBJ","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":"e4a3f0591ecb36b94e3925f9c58231f9a058fcf8180ddf1524063fa01f8ea97a","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-16T12:58:23Z","title_canon_sha256":"f25a6989dee1b357251c7bdf75e44efa743378dfa05b85413adbaf18413b1b72"},"schema_version":"1.0","source":{"id":"1506.08764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08764","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08764v1","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08764","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"CF3QSD6IUGL6","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CF3QSD6IUGL6RLNR","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CF3QSD6I","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:9bf05c12342a9de1685d02a2acdf7ac66636ef9efd3806cc9ffe5642eea8bb97","target":"graph","created_at":"2026-05-18T00:32:36Z","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":"It is well-known that Einstein gravity is kinematic (no non-trivial vacuum solution;i.e. Riemann vanishes whenever Ricci does so) in $3$ dimension because Riemann is entirely given in terms of Ricci. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one $N$th order term in action) gravity for which $N$th order Lovelock Riemann tensor is indeed given in terms of corresponding Ricci for all odd $d=2N+1$ dimensions. This feature of gravity is realized only in higher dimensions a","authors_text":"Naresh Dadhich","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-16T12:58:23Z","title":"A discerning gravitational property for gravitational equation in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08764","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:e7512da3533f12a269122aa003a872b8607c5b1f19308aa4820a5a33e67d6505","target":"record","created_at":"2026-05-18T00:32:36Z","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":"e4a3f0591ecb36b94e3925f9c58231f9a058fcf8180ddf1524063fa01f8ea97a","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-16T12:58:23Z","title_canon_sha256":"f25a6989dee1b357251c7bdf75e44efa743378dfa05b85413adbaf18413b1b72"},"schema_version":"1.0","source":{"id":"1506.08764","kind":"arxiv","version":1}},"canonical_sha256":"1177090fc8a197e8adb1f49a83fb160a6ca1f27cfaec18d3d0de4ca03540f28e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1177090fc8a197e8adb1f49a83fb160a6ca1f27cfaec18d3d0de4ca03540f28e","first_computed_at":"2026-05-18T00:32:36.632703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:36.632703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kgpI/2CpBfmRVS5TVI/k91kXkCi+Wj36brn6MPzAlnnF63FEQmHLDpM8x2SnJSm9h20cnH4PKzV7GL2bx9PaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:36.633394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7512da3533f12a269122aa003a872b8607c5b1f19308aa4820a5a33e67d6505","sha256:9bf05c12342a9de1685d02a2acdf7ac66636ef9efd3806cc9ffe5642eea8bb97"],"state_sha256":"58e42d50c7d001c48f7852f6f6db6ce81d8b633179944c0e71d0a5917cd5a22a"}