{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VY6GTIVBRWALLBDTNQRHZFWVEF","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":"8acf6bbcec9d81878e5a11651feee58b4d29c3b9cc14b24760d7daa20ae77704","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2010-05-31T05:58:47Z","title_canon_sha256":"5dfb0ca335af473686e8b99b78acb207d1225ab3b030db1bbae81f7741f95df6"},"schema_version":"1.0","source":{"id":"1005.5590","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5590","created_at":"2026-05-18T02:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5590v1","created_at":"2026-05-18T02:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5590","created_at":"2026-05-18T02:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"VY6GTIVBRWAL","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VY6GTIVBRWALLBDT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VY6GTIVB","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:8fb39ede4ec91c1127096fb60fa1e5bb5fd2712dccd5a6b82dacaa5b14fe7557","target":"graph","created_at":"2026-05-18T02:07:06Z","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 this paper, we study Randers metrics and find a condition on Ricci tensor of these metrics to be Berwaldian. This generalize Shen's Theorem which says: every R-{\\deg}at complete Randers metric is locally Minkowskian. Then we find a necessary and sufficient condition on Ricci tensor under which a Randers metric of scalar {\\deg}ag curvature is of zero {\\deg}ag curvature.","authors_text":"A. Tayebi, E. Peyghan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2010-05-31T05:58:47Z","title":"On Ricci-Tensor of Randers Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5590","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:b162859c2382e4fa517f20abeffd4fe8c1aa92ae156c8a047ddaafcad8a1b4d0","target":"record","created_at":"2026-05-18T02:07:06Z","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":"8acf6bbcec9d81878e5a11651feee58b4d29c3b9cc14b24760d7daa20ae77704","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2010-05-31T05:58:47Z","title_canon_sha256":"5dfb0ca335af473686e8b99b78acb207d1225ab3b030db1bbae81f7741f95df6"},"schema_version":"1.0","source":{"id":"1005.5590","kind":"arxiv","version":1}},"canonical_sha256":"ae3c69a2a18d80b584736c227c96d5217c208f90f2d816683e13f0aa79f91059","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae3c69a2a18d80b584736c227c96d5217c208f90f2d816683e13f0aa79f91059","first_computed_at":"2026-05-18T02:07:06.429173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:06.429173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AWap9X9qDE4wncHtbXc9UMCW9LzqPAI6Ss2WAlfviTL3Wuv0egybTQkSKKSFFW3nhq/8fboKduayyrJIWoVRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:06.429689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5590","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b162859c2382e4fa517f20abeffd4fe8c1aa92ae156c8a047ddaafcad8a1b4d0","sha256:8fb39ede4ec91c1127096fb60fa1e5bb5fd2712dccd5a6b82dacaa5b14fe7557"],"state_sha256":"e1c11fb61308fd065195689ad62964686eeb059f31660b0f5df04739df6cbbcc"}