{"paper":{"title":"The Capacity of a Family of Sticky Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mladen Kova\\v{c}evi\\'{c}","submitted_at":"2026-07-30T14:30:15Z","abstract_excerpt":"We determine the capacity of a family of $q$-ary sticky-insertion channels. Fix $q\\geq2$ and $d\\geq1$, and let $\\lambda$ be the unique positive solution of $\\lambda^d = (q-1) (\\lambda^{d-1} + \\cdots + \\lambda + 1 )$. We prove that, for every repetition law supported on $1+d\\mathbb{Z}_{\\geq0}$ and satisfying a coefficientwise-domination criterion with domination constant $\\gamma\\geq\\lambda^{-d}$, the Shannon capacity equals the zero-error capacity, both being $\\log_2\\lambda$ bits per symbol. We also exhibit explicit repetition laws satisfying these conditions, one of which is given by the weigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28281","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/2607.28281/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"}