{"paper":{"title":"On the recognition problem for limits of entropy functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Geva Yashfe","submitted_at":"2025-09-08T03:05:48Z","abstract_excerpt":"We prove that there is no algorithm to decide whether a given integer vector is in the closure of the entropic cone $\\overline{\\Gamma_{n}^{*}}$. Equivalently, there is no decision procedure to determine whether a given integer-valued function $h:\\mathcal{P}(\\{1,\\ldots,n\\})\\rightarrow\\mathbb{Z}_{\\ge 0}$ is a pointwise limit of joint entropy functions. In other words, given such an $h$, it is undecidable whether for all $\\varepsilon > 0$ there exists a finite probability space $(\\Omega,P)$ with random variables $X_{1},\\ldots,X_{n}$ such that their joint entropy $H$ satisfies $\\max_{I\\subseteq\\{1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06302","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/2509.06302/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"}