{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W7ZZ7NBGH3JFDUXBDW2PYLLPJ3","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":"04765ec294bd695096bcf049ede28ee54c9d5e11519d95cbcc79db068892b700","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-20T11:12:34Z","title_canon_sha256":"466806e7cbf38b5f61a129fbdc4ee462a78d40d7f1287649fcf99f611928466c"},"schema_version":"1.0","source":{"id":"1305.4498","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4498","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4498v3","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4498","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"W7ZZ7NBGH3JF","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W7ZZ7NBGH3JFDUXB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W7ZZ7NBG","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:456cb24970fb84583f1005c55898f0431b5a912ecb4d4de5e82e03670a1ca479","target":"graph","created_at":"2026-05-18T03:03:44Z","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 note, adopting the pullback formalism of global Finsler geometry, we show by a counterexample that the kernel $\\text{Ker}_R$ of the h-curvature $R$ of Cartan connection and the associated nullity distribution $\\N_R$ do not coincide, contrary to Akbar-Zadeh's result \\cite{akbar.nul3.}. We give sufficient conditions for $\\text{Ker}_R$ and $\\N_R$ to coincide.","authors_text":"Nabil L. Youssef, S. G. Elgendi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-20T11:12:34Z","title":"A note on \"Sur le noyau de l'op\\'{e}rateur de courbure d'une vari\\'{e}t\\'{e} finsl\\'{e}rienne\" [C. R. Acad. Sci. Paris, t. 272 (1971), 807-810]"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4498","kind":"arxiv","version":3},"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:d0d16099abd91d87366b73e1d2a3522dccc135815f6f63624cca0b118140fbfb","target":"record","created_at":"2026-05-18T03:03:44Z","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":"04765ec294bd695096bcf049ede28ee54c9d5e11519d95cbcc79db068892b700","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-20T11:12:34Z","title_canon_sha256":"466806e7cbf38b5f61a129fbdc4ee462a78d40d7f1287649fcf99f611928466c"},"schema_version":"1.0","source":{"id":"1305.4498","kind":"arxiv","version":3}},"canonical_sha256":"b7f39fb4263ed251d2e11db4fc2d6f4ec42183017e68983ba0a8ea9e4d414a2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7f39fb4263ed251d2e11db4fc2d6f4ec42183017e68983ba0a8ea9e4d414a2d","first_computed_at":"2026-05-18T03:03:44.345190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:44.345190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7h8WKHQk9I3AF/DwJ+wudqcvWW2tZAAfqGUBI4cwz8hWgXJt5baoSRno94AAs16aIsPytCd86F4hYLoWD8AaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:44.345995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4498","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0d16099abd91d87366b73e1d2a3522dccc135815f6f63624cca0b118140fbfb","sha256:456cb24970fb84583f1005c55898f0431b5a912ecb4d4de5e82e03670a1ca479"],"state_sha256":"b46ec02078b1e24b10cc47a937f454b66ff170ffcf1bda08c7e23ad7f1c77845"}