{"paper":{"title":"Fixed Points of the q-Bracket on the p-Adic Unit Disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eric Brussel","submitted_at":"2009-02-25T18:19:13Z","abstract_excerpt":"We study the fixed points of the q-bracket on the complex unit disk, and prove the following. The set of (nontrivial) pairs (x,q) such that [x]_q=x form a manifold whose standard projections both have degree p-2. There is an analytic function Q(X) taking x to q for which [x]_q=x, which is a (bijective) contraction unless the multiplicity of the residue of x in the fiber over q is two. The restriction of the theory to Z_p is trivial unless p=3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4284","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":""},"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"}