{"paper":{"title":"On the characterization of Peth\\H{o}'s Loudspeaker","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mario Weitzer","submitted_at":"2014-10-28T15:43:08Z","abstract_excerpt":"For $d \\in \\mathbb{N}$ and $\\mathbf{r} \\in \\mathbb{C}^d$ let $\\gamma_\\mathbf{r}: \\mathbb{Z}[\\mathrm{i}]^d \\to \\mathbb{Z}[\\mathrm{i}]^d$, where $\\gamma_\\mathbf{r}(\\mathbf{a})=(a_2,...,a_d,$ $-\\lfloor\\mathbf{r}\\mathbf{a}\\rfloor)$ for $\\mathbf{a}=(a_1,...,a_d)$, denote the (d-dimensional) Gaussian shift radix system associated with $\\mathbf{r}$. $\\gamma_\\mathbf{r}$ is said to have the finiteness property iff all orbits of $\\gamma_\\mathbf{r}$ end up in $(0,...,0)$; the set of all corresponding $\\mathbf{r} \\in \\mathbb{C}^d$ is denoted by $\\mathcal{G}_{d}^{(0)}$. It has a very complicated structure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7667","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":""},"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"}