{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DZX4HT6SWPO7TH5LRHW7QZ5QJL","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":"3d72312968c5fddbda41e0ec98aabb9b7be43cd01ceb67ee81b547c88f8550a1","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-25T20:33:28Z","title_canon_sha256":"a09274c78dcf68fceae5735ed85e3c9345420c281cdbad4ab77b77a7d7867eec"},"schema_version":"1.0","source":{"id":"1607.07468","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07468","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07468v2","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07468","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"DZX4HT6SWPO7","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DZX4HT6SWPO7TH5L","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DZX4HT6S","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:735a9a19aa4b88b76dafdabdf8ca28afec99f0343b081375f9eda8f37c63eeb2","target":"graph","created_at":"2026-05-18T01:09:54Z","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 pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of recurrence are studied. The generalized concircular recurrence, as a new concept, is singled out.","authors_text":"A. Soleiman, Nabil L. Youssef","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-25T20:33:28Z","title":"Some Types of Recurrence in Finsler geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07468","kind":"arxiv","version":2},"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":"sha256:42cbf6264bdc2796e5c229036b9431852da78b49a51cd604707a9c4224de0fc0","target":"record","created_at":"2026-05-18T01:09:54Z","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":"3d72312968c5fddbda41e0ec98aabb9b7be43cd01ceb67ee81b547c88f8550a1","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-25T20:33:28Z","title_canon_sha256":"a09274c78dcf68fceae5735ed85e3c9345420c281cdbad4ab77b77a7d7867eec"},"schema_version":"1.0","source":{"id":"1607.07468","kind":"arxiv","version":2}},"canonical_sha256":"1e6fc3cfd2b3ddf99fab89edf867b04ac398a402babfa66f04a0ef2e8c0ea090","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e6fc3cfd2b3ddf99fab89edf867b04ac398a402babfa66f04a0ef2e8c0ea090","first_computed_at":"2026-05-18T01:09:54.461662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:54.461662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i42ort8KyKITlVSnos+tAXMp/KVKBO3he4rjnJCZbb5v7fPwu36ksS2MCfv7PY9SIJphvPvAPhHdht3fB90EAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:54.462278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07468","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42cbf6264bdc2796e5c229036b9431852da78b49a51cd604707a9c4224de0fc0","sha256:735a9a19aa4b88b76dafdabdf8ca28afec99f0343b081375f9eda8f37c63eeb2"],"state_sha256":"ebe21cff3bcb72355dfde45f368222c9344c9f1784bbb986f5ca4c8f9da22044"}