{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BKGJEDW75WJEL4RXJOMQUOMI2D","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":"e3e0dadf169e9f0f2ba0b307e0f7d755acca0c3063863cc83fb4b0c6610f5466","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-19T11:30:56Z","title_canon_sha256":"92e53fedeafa86e5460bed90e879a9fa9075fab7002250bddd4e26d94bfc35fe"},"schema_version":"1.0","source":{"id":"1305.4629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4629","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4629v1","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4629","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"pith_short_12","alias_value":"BKGJEDW75WJE","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BKGJEDW75WJEL4RX","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BKGJEDW7","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:ec3bfdf087d0ab9c03531e3db59b1b3996fa868580825a39759b08ab9c4a20b7","target":"graph","created_at":"2026-05-18T03:25:15Z","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 a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag curvature and find a condition under which these metrics reduce to C-reducible metrics. This generalize Matsumotos theorem, which describes the equivalency of C-reducibility and P-reducibility on Finsler manifolds with scalar curvature. Then we show that generalized P-reducible metrics with vanishing stretch curvature are C-reducible.","authors_text":"A. Heydari, A. Tayebi, E. Peyghan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-19T11:30:56Z","title":"Generalized P-Reducible Finsler Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4629","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":"sha256:4cbe732e8b800eeab7d6bd002d2ce59187fead1af034c817757d52d1fc2ceb66","target":"record","created_at":"2026-05-18T03:25:15Z","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":"e3e0dadf169e9f0f2ba0b307e0f7d755acca0c3063863cc83fb4b0c6610f5466","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-19T11:30:56Z","title_canon_sha256":"92e53fedeafa86e5460bed90e879a9fa9075fab7002250bddd4e26d94bfc35fe"},"schema_version":"1.0","source":{"id":"1305.4629","kind":"arxiv","version":1}},"canonical_sha256":"0a8c920edfed9245f2374b990a3988d0d202ac74705b60cd7c71ccc03fb60daf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a8c920edfed9245f2374b990a3988d0d202ac74705b60cd7c71ccc03fb60daf","first_computed_at":"2026-05-18T03:25:15.565779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:15.565779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YDerQ2JqH+0R3X0UnWf/ly51u/1IV6dkafNmUv/Tbw9PNGS3xpuBtQRPLSyYnDKL7qcGGzzNQpdpJRN+QffoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:15.566377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cbe732e8b800eeab7d6bd002d2ce59187fead1af034c817757d52d1fc2ceb66","sha256:ec3bfdf087d0ab9c03531e3db59b1b3996fa868580825a39759b08ab9c4a20b7"],"state_sha256":"0cd58a11b609befc932550abff326e45b3edb8c8433e346282747148ecdb15b3"}