{"paper":{"title":"An integral weight realization theorem for subset currents on free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich","submitted_at":"2012-11-26T01:33:27Z","abstract_excerpt":"We prove that if $N\\ge 2$ and $\\alpha: F_N\\to \\pi_1(\\Gamma)$ is a marking on $F_N$, then for any integer $r\\ge 2$ and any $F_N$-invariant collection of non-negative integral \"weights\" associated to all subtrees $K$ of $\\widetilde \\Gamma$ of radius $\\le r$ satisfying some natural \"switch\" conditions, there exists a finite cyclically reduced folded $\\Gamma$-graph $\\Delta$ realizing these weights as numbers of \"occurrences\" of $K$ in $\\Delta$. As an application, we give a new, more direct and explicit, proof of one of the main results of our paper with Nagnibeda \\cite{KN3} stating that for any $N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5836","kind":"arxiv","version":4},"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"}