{"paper":{"title":"From some Pisot numerations to topological groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.FL","math.NT"],"primary_cat":"math.DS","authors_text":"Jake Sudbery, Olivier Carton, Reem Yassawi","submitted_at":"2026-06-29T16:02:02Z","abstract_excerpt":"A Pisot numeration system $U$ for $\\mathbb N$ is a sequence of natural numbers\n  generated by an integral homogeneous linear recurrence whose\n  characteristic polynomial is the minimal polynomial of a Pisot number.\n  The purpose of this paper is to introduce the analogue of the group of\n  $p$-adic integers for such numerations when they \\emph{preserve zeros},\n  which is equivalent to the `Condition F' introduced by Frougny and\n  Solomyak for $\\beta$-numerations. We show that these topological groups $\\mathbb Z_U$\n  project homomorphically onto a torus. Equipping $\\mathbb Z_U$ with the\n  approp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30496","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/2606.30496/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"}