{"paper":{"title":"Overgroups of the arboreal representation of PCF polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Wayne Peng","submitted_at":"2025-05-31T08:22:44Z","abstract_excerpt":"Consider a number field $K$ and a rational function $f$ of degree greater than 1 over $K$. By taking preimages of $\\alpha\\in K$ under successive iterates of $f$, an infinite $d$-ary tree $T_\\infty$ rooted at $\\alpha$ can be constructed. An edge is assigned between two preimages $x$ and $y$ if $f(x)=y$. The absolute Galois group of $K$, acting on $T_\\infty$ through tree automorphisms, generates a subgroup $\\text{Gal}_f^\\infty(\\alpha)$ in the group of all automorphisms of $T_\\infty$, $\\text{Aut}(T_\\infty)$.\n  We have discovered a new class of natural overgroups in which the image of the Galois r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00456","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/2506.00456/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"}