{"paper":{"title":"The Collatz Conjecture & Non-Archimedean Spectral Theory: Part I -- Arithmetic Dynamical Systems and Non-Archimedean Value Distribution Theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Maxwell Charles Siegel","submitted_at":"2020-07-19T00:09:29Z","abstract_excerpt":"Let $q$ be an odd prime, and let $T_{q}:\\mathbb{Z}\\rightarrow\\mathbb{Z}$ be the Shortened $qx+1$ map, defined by $T_{q}\\left(n\\right)=n/2$ if $n$ is even and $T_{q}\\left(n\\right)=\\left(qn+1\\right)/2$ if $n$ is odd. The study of the dynamics of these maps is infamous for its difficulty, with the characterization of the dynamics of $T_{3}$ being an alternative formulation of the famous Collatz Conjecture. This series of papers presents a new paradigm for studying such arithmetic dynamical systems by way of a neglected area of ultrametric analysis which we have termed $\\left(p,q\\right)$-adic anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.15936","kind":"arxiv","version":3},"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/2007.15936/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"}