{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:E7MSXT4FN6ZUWXKYQYFWF3OHJ4","short_pith_number":"pith:E7MSXT4F","schema_version":"1.0","canonical_sha256":"27d92bcf856fb34b5d58860b62edc74f14d13e5ba100d8efc77499b58120114a","source":{"kind":"arxiv","id":"1604.06659","version":1},"attestation_state":"computed","paper":{"title":"On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Julius Fergy T. Rabago","submitted_at":"2016-04-22T14:00:07Z","abstract_excerpt":"The purpose of this paper is twofold. First, we derive theoretically, using appropriate transformation on $x_n$, the closed-form solution of the nonlinear difference equation \\[ x_{n+1} = \\frac{1}{\\pm 1 + x_n},\\qquad n\\in \\mathbb{N}_0. \\] We mention that the solution form of this equation was already obtained by Tollu et al. in 2013, but through induction principle, and one of our purpose is to clearly explain how was the formula appeared in such structure. After that, with the solution form of the above equation at hand, we prove a case of Sroysang's conjecture (2013); i.e., given a fixed pos"},"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":"1604.06659","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-22T14:00:07Z","cross_cats_sorted":[],"title_canon_sha256":"f58d0352ffa7b363ddae4c123a4aeeda9ee7f9dff3ad02f792376e74ca7aee7a","abstract_canon_sha256":"e9783ee7db46c034d0cd871bbf297f1f6f26463ffa5eb426cc04aca5e5c19fd8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:28.494038Z","signature_b64":"tWhIwFpW6IZP4Soibqud8/p9TVN6cHzCPgMWskbbhFoIbRGPsWyABboXJV5+ZeaPzpiGZRkOvDiOqTeQ8n7cBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27d92bcf856fb34b5d58860b62edc74f14d13e5ba100d8efc77499b58120114a","last_reissued_at":"2026-05-18T01:16:28.493461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:28.493461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Julius Fergy T. Rabago","submitted_at":"2016-04-22T14:00:07Z","abstract_excerpt":"The purpose of this paper is twofold. First, we derive theoretically, using appropriate transformation on $x_n$, the closed-form solution of the nonlinear difference equation \\[ x_{n+1} = \\frac{1}{\\pm 1 + x_n},\\qquad n\\in \\mathbb{N}_0. \\] We mention that the solution form of this equation was already obtained by Tollu et al. in 2013, but through induction principle, and one of our purpose is to clearly explain how was the formula appeared in such structure. After that, with the solution form of the above equation at hand, we prove a case of Sroysang's conjecture (2013); i.e., given a fixed pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06659","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":"1604.06659","created_at":"2026-05-18T01:16:28.493571+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.06659v1","created_at":"2026-05-18T01:16:28.493571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06659","created_at":"2026-05-18T01:16:28.493571+00:00"},{"alias_kind":"pith_short_12","alias_value":"E7MSXT4FN6ZU","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"E7MSXT4FN6ZUWXKY","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"E7MSXT4F","created_at":"2026-05-18T12:30:12.583610+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.09987","citing_title":"On the Solutions of Systems of Difference Equations via Tribonacci Numbers","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4","json":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4.json","graph_json":"https://pith.science/api/pith-number/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/graph.json","events_json":"https://pith.science/api/pith-number/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/events.json","paper":"https://pith.science/paper/E7MSXT4F"},"agent_actions":{"view_html":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4","download_json":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4.json","view_paper":"https://pith.science/paper/E7MSXT4F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.06659&json=true","fetch_graph":"https://pith.science/api/pith-number/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/graph.json","fetch_events":"https://pith.science/api/pith-number/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/action/storage_attestation","attest_author":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/action/author_attestation","sign_citation":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/action/citation_signature","submit_replication":"https://pith.science/pith/E7MSXT4FN6ZUWXKYQYFWF3OHJ4/action/replication_record"}},"created_at":"2026-05-18T01:16:28.493571+00:00","updated_at":"2026-05-18T01:16:28.493571+00:00"}