{"paper":{"title":"Elementary solutions of ordinary tropical differential equations, and vanishing orders of solutions of algebraic differential equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Carla Valencia-Negrete, Cristhian Garay-L\\'opez, Johana Luviano-Flores","submitted_at":"2026-06-20T01:35:16Z","abstract_excerpt":"Our aim is to use tropical differential algebra to systematically build a combinatorial basis for the study of the set of (formal) power series solutions to nonlinear algebraic ordinary differential equations (over $\\mathbb{C}$) expanded around the point $t_0=0\\in\\mathbb{C}$, which may also be effectively computed using standard tropical algebra.\n  This paper is divided into two parts. First, given an ordinary tropical differential equation in one differential variable $P=P(y)$ of (differential) order $k$, we study the sets $Sol_{\\mathbb{B}[\\![t^{\\Gamma}]\\!],k}(P)\\supset \\mu(Sol_{\\mathbb{B}[\\!"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21829","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/2606.21829/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"}