{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:W5Y4R2GJKHHJR4PSCAL5OIZWGM","short_pith_number":"pith:W5Y4R2GJ","schema_version":"1.0","canonical_sha256":"b771c8e8c951ce98f1f21017d723363318ce2317e1cc2486726ab717c92ebd4a","source":{"kind":"arxiv","id":"1906.09987","version":1},"attestation_state":"computed","paper":{"title":"On the Solutions of Systems of Difference Equations via Tribonacci Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"\\.Inci Okumu\\c{s}, Y\\\"uksel Soykan","submitted_at":"2019-06-24T14:19:18Z","abstract_excerpt":"The main objective of this paper is to investigate the explicit form, stability character and global behavior of solutions of the following two systems of rational difference equations\n  x_{n+1}=((+(-)1)/(y_{n}(x_{n-1}+(-)1)+1)), y_{n+1}=((+(-)1)/(x_{n}(y_{n-1}+(-)1)+1)), n=0,1,...\n  such that their solutions are associated with Tribonacci numbers."},"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":"1906.09987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-24T14:19:18Z","cross_cats_sorted":[],"title_canon_sha256":"5f6da78cc7fdcff57b656a5daab4c732feddfa754933bb516e76fe863045193f","abstract_canon_sha256":"3ecc378f6f3806cb64c87740ed1755433c874b4341a13528a886d56d33c6c39c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:35.832963Z","signature_b64":"5i2D2kP0JdmvhN58Q+Lb43b+PYzE9ExJIuC4QdNl1sznI3+SM4MIdGeeAfdEjdjkFjURMX+SW1/vDMHNb+KzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b771c8e8c951ce98f1f21017d723363318ce2317e1cc2486726ab717c92ebd4a","last_reissued_at":"2026-05-17T23:42:35.832199Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:35.832199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Solutions of Systems of Difference Equations via Tribonacci Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"\\.Inci Okumu\\c{s}, Y\\\"uksel Soykan","submitted_at":"2019-06-24T14:19:18Z","abstract_excerpt":"The main objective of this paper is to investigate the explicit form, stability character and global behavior of solutions of the following two systems of rational difference equations\n  x_{n+1}=((+(-)1)/(y_{n}(x_{n-1}+(-)1)+1)), y_{n+1}=((+(-)1)/(x_{n}(y_{n-1}+(-)1)+1)), n=0,1,...\n  such that their solutions are associated with Tribonacci numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09987","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":"1906.09987","created_at":"2026-05-17T23:42:35.832383+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.09987v1","created_at":"2026-05-17T23:42:35.832383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09987","created_at":"2026-05-17T23:42:35.832383+00:00"},{"alias_kind":"pith_short_12","alias_value":"W5Y4R2GJKHHJ","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"W5Y4R2GJKHHJR4PS","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"W5Y4R2GJ","created_at":"2026-05-18T12:33:30.264802+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/W5Y4R2GJKHHJR4PSCAL5OIZWGM","json":"https://pith.science/pith/W5Y4R2GJKHHJR4PSCAL5OIZWGM.json","graph_json":"https://pith.science/api/pith-number/W5Y4R2GJKHHJR4PSCAL5OIZWGM/graph.json","events_json":"https://pith.science/api/pith-number/W5Y4R2GJKHHJR4PSCAL5OIZWGM/events.json","paper":"https://pith.science/paper/W5Y4R2GJ"},"agent_actions":{"view_html":"https://pith.science/pith/W5Y4R2GJKHHJR4PSCAL5OIZWGM","download_json":"https://pith.science/pith/W5Y4R2GJKHHJR4PSCAL5OIZWGM.json","view_paper":"https://pith.science/paper/W5Y4R2GJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.09987&json=true","fetch_graph":"https://pith.science/api/pith-number/W5Y4R2GJKHHJR4PSCAL5OIZWGM/graph.json","fetch_events":"https://pith.science/api/pith-number/W5Y4R2GJKHHJR4PSCAL5OIZWGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W5Y4R2GJKHHJR4PSCAL5OIZWGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W5Y4R2GJKHHJR4PSCAL5OIZWGM/action/storage_attestation","attest_author":"https://pith.science/pith/W5Y4R2GJKHHJR4PSCAL5OIZWGM/action/author_attestation","sign_citation":"https://pith.science/pith/W5Y4R2GJKHHJR4PSCAL5OIZWGM/action/citation_signature","submit_replication":"https://pith.science/pith/W5Y4R2GJKHHJR4PSCAL5OIZWGM/action/replication_record"}},"created_at":"2026-05-17T23:42:35.832383+00:00","updated_at":"2026-05-17T23:42:35.832383+00:00"}