{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PX2L5FP22C6CLUKBS4PM6P3O57","short_pith_number":"pith:PX2L5FP2","schema_version":"1.0","canonical_sha256":"7df4be95fad0bc25d141971ecf3f6eefe0858e67f440f127a3577153be2542f0","source":{"kind":"arxiv","id":"1902.06520","version":1},"attestation_state":"computed","paper":{"title":"On certain rational recursive sequences of order four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Darlison Nyirenda, Mensah Folly-Gbetoula","submitted_at":"2019-02-18T11:23:27Z","abstract_excerpt":"We obtain solutions to the recursive sequences of the form $$x_{n + 1} = \\frac{x_{n - 3}x_{n }}{x_{n - 2}(a_n + b_nx_{n -3}x_{n})}$$ where $a_n$ and $b_n$ are arbitrary sequences of real numbers, and the initial values are gives as; $x_{-3},x_{-2}, x_{-1}$ and $x_{0}$. Our methodology is to employ a group theoretic method which lowers the order of the equations, and then solve the resulting lower order recurrence relations that arise therefrom."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.06520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-18T11:23:27Z","cross_cats_sorted":[],"title_canon_sha256":"1bcc08cbdd1299f071d98743b0509f1f1d6880ea439b8b8af8b071927d88f394","abstract_canon_sha256":"c8e1df4594ecb3240ef4dc896a9126df4f3147068853f7a5fbac1f4bb9a0b143"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:45.225777Z","signature_b64":"tpAb4gPC4QcR5UVz8vY7ulOmiAMvLnvACVnDLd1zt1g87nFDz+9KNolTVw3VyEjkSVc0XW+93xqpvawdyseQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7df4be95fad0bc25d141971ecf3f6eefe0858e67f440f127a3577153be2542f0","last_reissued_at":"2026-05-17T23:53:45.225134Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:45.225134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On certain rational recursive sequences of order four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Darlison Nyirenda, Mensah Folly-Gbetoula","submitted_at":"2019-02-18T11:23:27Z","abstract_excerpt":"We obtain solutions to the recursive sequences of the form $$x_{n + 1} = \\frac{x_{n - 3}x_{n }}{x_{n - 2}(a_n + b_nx_{n -3}x_{n})}$$ where $a_n$ and $b_n$ are arbitrary sequences of real numbers, and the initial values are gives as; $x_{-3},x_{-2}, x_{-1}$ and $x_{0}$. Our methodology is to employ a group theoretic method which lowers the order of the equations, and then solve the resulting lower order recurrence relations that arise therefrom."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06520","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.06520","created_at":"2026-05-17T23:53:45.225231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.06520v1","created_at":"2026-05-17T23:53:45.225231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06520","created_at":"2026-05-17T23:53:45.225231+00:00"},{"alias_kind":"pith_short_12","alias_value":"PX2L5FP22C6C","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"PX2L5FP22C6CLUKB","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"PX2L5FP2","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57","json":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57.json","graph_json":"https://pith.science/api/pith-number/PX2L5FP22C6CLUKBS4PM6P3O57/graph.json","events_json":"https://pith.science/api/pith-number/PX2L5FP22C6CLUKBS4PM6P3O57/events.json","paper":"https://pith.science/paper/PX2L5FP2"},"agent_actions":{"view_html":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57","download_json":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57.json","view_paper":"https://pith.science/paper/PX2L5FP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.06520&json=true","fetch_graph":"https://pith.science/api/pith-number/PX2L5FP22C6CLUKBS4PM6P3O57/graph.json","fetch_events":"https://pith.science/api/pith-number/PX2L5FP22C6CLUKBS4PM6P3O57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57/action/storage_attestation","attest_author":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57/action/author_attestation","sign_citation":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57/action/citation_signature","submit_replication":"https://pith.science/pith/PX2L5FP22C6CLUKBS4PM6P3O57/action/replication_record"}},"created_at":"2026-05-17T23:53:45.225231+00:00","updated_at":"2026-05-17T23:53:45.225231+00:00"}