{"paper":{"title":"The Minkowski dimension of the image of an arboreal Galois representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chifan Leung, Clayton Petsche","submitted_at":"2025-12-21T17:18:26Z","abstract_excerpt":"We consider the Minkowski dimension of the arboreal Galois group $G_{f,\\alpha}$ associated to a rational map $f:\\mathbb{P}^1\\to\\mathbb{P}^1$ and a base point $\\alpha\\in\\mathbb{P}^1(K)$. This is a subgroup of the automorphism group of the infinite $d$-ary rooted tree whose vertices are indexed by the backward orbit $f^{-\\infty}(\\alpha)$. We show that the Minkowski dimension exists for the profinite iterated monodromy groups $G_f^\\mathrm{arith}$ and $G_f^\\mathrm{geom}$, and that these two groups have the same dimension. We prove a dichotomy theorem stating that $G_f^\\mathrm{arith}$ and $G_f^\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.18825","kind":"arxiv","version":2},"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/2512.18825/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"}