{"paper":{"title":"The Construction of Near-optimal Universal Coding of Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Wei Yan, Yunghsiang S. Han","submitted_at":"2025-07-31T01:21:06Z","abstract_excerpt":"The Universal Coding of Integers~(UCI) is suitable for discrete memoryless sources with unknown probability distributions and infinitely countable alphabet sizes. A UCI is a class of prefix codes for which the ratio of the average codeword length to $\\max\\{1,H(P)\\}$ is within a constant expansion factor \\textcolor{red}{$C_{\\mathcal{C}}$} for any decreasing probability distribution $P$, where $H(P)$ is the entropy of $P$. For any UCI code $\\mathcal{C}$, \\emph{the minimum expansion factor} \\textcolor{red}{$C_{\\mathcal{C}}^{*}$} is defined to represent the infimum of the set of extension factors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23180","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"}