{"paper":{"title":"On difference-differential Lax pairs and integrals of Painlev\\'e equations in finite characteristic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"nlin.SI","authors_text":"Nalini Joshi, Pieter Roffelsen, Tomas Lasic Latimer","submitted_at":"2026-07-08T04:02:50Z","abstract_excerpt":"We collect rank two difference-differential Lax pairs for classical Painlev\\'e equations in the literature and put each in $2\\times 2$ matrix form with the coefficient matrix of the spectral equation a degree two matrix polynomial. We describe and apply a general method to obtain integrals of motion in characteristic $p$ from these Lax pairs. For every relevant Painlev\\'e equation, this leads to a countable list of integrals of motion, with one entry for each prime $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06980","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06980/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}