{"paper":{"title":"On definable groups in dp-minimal topological fields equipped with a generic derivation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Fran\\c{c}oise Point","submitted_at":"2025-05-11T16:32:57Z","abstract_excerpt":"Let $T$ be a complete, model-complete, geometric dp-minimal $\\mathcal{L}$-theory of topological fields of characteristic $0$ and let $T(\\partial)$ be the theory of expansions of models of $T$ by a derivation $\\partial$. We assume that $T(\\partial)$ has a model-companion $T_{\\partial}$. Let $\\Gamma$ be a finite-dimensional $\\mathcal{L}_\\partial$-definable group in a model of $T_\\partial$. Then we show that $\\Gamma$ densely and definably embeds in an $\\mathcal{L}$-definable group $G$.\n  Further, using a $C^1$-cell decomposition result, we show that $\\Gamma$ densely and definably embeds in a defi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07044","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/2505.07044/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"}