{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:SRUWAUTQX7AFZYODBDES32EBJW","short_pith_number":"pith:SRUWAUTQ","schema_version":"1.0","canonical_sha256":"9469605270bfc05ce1c308c92de8814d816af25cbb380ccdda79dba05ef47c2f","source":{"kind":"arxiv","id":"solv-int/9409002","version":1},"attestation_state":"computed","paper":{"title":"New exact solutions for the discrete fourth Painlev\\'e equation","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"solv-int","authors_text":"Andrew P. Bassom, Exeter, Peter A. Clarkson (Department of Mathematics, U.K.), University of Exeter","submitted_at":"1994-09-16T15:32:03Z","abstract_excerpt":"In this paper we derive a number of exact solutions of the discrete equation $$x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})= {-2z_nx_n^3+(\\eta-3\\delta^{-2}-z_n^2)x_n^2+\\mu^2\\over (x_n+z_n+\\gamma)(x_n+z_n-\\gamma)},\\eqno(1)$$ where $z_n=n\\delta$ and $\\eta$, $\\delta$, $\\mu$ and $\\gamma$ are constants. In an appropriate limit (1) reduces to the fourth \\p\\ (PIV) equation $${\\d^2w\\over\\d z^2} = {1\\over2w}\\left({\\d w\\over\\d z}\\right)^2+\\tfr32w^3 + 4zw^2 + 2(z^2-\\alpha)w +{\\beta\\over w},\\eqno(2)$$ where $\\alpha$ and $\\beta$ are constants and (1) is commonly referred to as the discretised fourth Painlev\\'e equa"},"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":"solv-int/9409002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"solv-int","submitted_at":"1994-09-16T15:32:03Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"b69a6a71896ce9fb7df90655660ef0991b451a0a716e64f5fac36032ecd13730","abstract_canon_sha256":"ea04052633439ee4e041953493c32cfb611b30d53707319d230fcc91ec6b44e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:52.141341Z","signature_b64":"6Hc3uuWobdgazMRGDg3Jd0K0uByNqgEQaxWxMiQc1DQk3Rq8KJZHGlxYtn0R/4R9wF6vVc72/LGtY4OhR072BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9469605270bfc05ce1c308c92de8814d816af25cbb380ccdda79dba05ef47c2f","last_reissued_at":"2026-05-18T01:37:52.140343Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:52.140343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New exact solutions for the discrete fourth Painlev\\'e equation","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"solv-int","authors_text":"Andrew P. Bassom, Exeter, Peter A. Clarkson (Department of Mathematics, U.K.), University of Exeter","submitted_at":"1994-09-16T15:32:03Z","abstract_excerpt":"In this paper we derive a number of exact solutions of the discrete equation $$x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})= {-2z_nx_n^3+(\\eta-3\\delta^{-2}-z_n^2)x_n^2+\\mu^2\\over (x_n+z_n+\\gamma)(x_n+z_n-\\gamma)},\\eqno(1)$$ where $z_n=n\\delta$ and $\\eta$, $\\delta$, $\\mu$ and $\\gamma$ are constants. 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