{"paper":{"title":"$p$-adic integrable systems: from biquadratic equations to local models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SG","authors_text":"\\'Alvaro Pelayo, Luis Crespo","submitted_at":"2026-06-23T09:52:37Z","abstract_excerpt":"Let $p$ be a prime number and $n$ a positive integer. The study of normal forms of $p$-adic analytic integrable systems $F=(f_1,\\ldots,f_n):(M,\\omega)\\to(\\mathbb{Q}_p)^n$ is essential to understand their geometrical and dynamical properties. Even though in some cases, such as dimension $4$, there is a classification of the local normal forms, it can be a challenge to determine them explicitly. Our goal in this paper is to introduce techniques to compute information about these local normal forms. We then explain how this is useful for instance to study the $p$-coupled angular momentum. The tec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24363","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/2606.24363/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"}