{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:SRUWAUTQX7AFZYODBDES32EBJW","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":"ea04052633439ee4e041953493c32cfb611b30d53707319d230fcc91ec6b44e0","cross_cats_sorted":["nlin.SI"],"license":"","primary_cat":"solv-int","submitted_at":"1994-09-16T15:32:03Z","title_canon_sha256":"b69a6a71896ce9fb7df90655660ef0991b451a0a716e64f5fac36032ecd13730"},"schema_version":"1.0","source":{"id":"solv-int/9409002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"solv-int/9409002","created_at":"2026-05-18T01:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"solv-int/9409002v1","created_at":"2026-05-18T01:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.solv-int/9409002","created_at":"2026-05-18T01:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"SRUWAUTQX7AF","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"SRUWAUTQX7AFZYOD","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"SRUWAUTQ","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:a6d6bbf8e86ee4dec2ebcb0853a3d8a3182b1c62030564319304071013067c25","target":"graph","created_at":"2026-05-18T01:37:52Z","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":"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","authors_text":"Andrew P. Bassom, Exeter, Peter A. Clarkson (Department of Mathematics, U.K.), University of Exeter","cross_cats":["nlin.SI"],"headline":"","license":"","primary_cat":"solv-int","submitted_at":"1994-09-16T15:32:03Z","title":"New exact solutions for the discrete fourth Painlev\\'e equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"solv-int/9409002","kind":"arxiv","version":1},"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":"sha256:714e12b11b2a66f609b5b122b74bce342762061eee3a0fb60998a91da354e7be","target":"record","created_at":"2026-05-18T01:37:52Z","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":"ea04052633439ee4e041953493c32cfb611b30d53707319d230fcc91ec6b44e0","cross_cats_sorted":["nlin.SI"],"license":"","primary_cat":"solv-int","submitted_at":"1994-09-16T15:32:03Z","title_canon_sha256":"b69a6a71896ce9fb7df90655660ef0991b451a0a716e64f5fac36032ecd13730"},"schema_version":"1.0","source":{"id":"solv-int/9409002","kind":"arxiv","version":1}},"canonical_sha256":"9469605270bfc05ce1c308c92de8814d816af25cbb380ccdda79dba05ef47c2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9469605270bfc05ce1c308c92de8814d816af25cbb380ccdda79dba05ef47c2f","first_computed_at":"2026-05-18T01:37:52.140343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:52.140343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Hc3uuWobdgazMRGDg3Jd0K0uByNqgEQaxWxMiQc1DQk3Rq8KJZHGlxYtn0R/4R9wF6vVc72/LGtY4OhR072BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:52.141341Z","signed_message":"canonical_sha256_bytes"},"source_id":"solv-int/9409002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:714e12b11b2a66f609b5b122b74bce342762061eee3a0fb60998a91da354e7be","sha256:a6d6bbf8e86ee4dec2ebcb0853a3d8a3182b1c62030564319304071013067c25"],"state_sha256":"f871c315974f9b59871849c2edafc011c51c7d76f1d3f69546e7ba41433ab2f4"}