{"paper":{"title":"Four-dimensional operator systems without the lifting property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Samuel J. Harris","submitted_at":"2025-07-31T19:06:43Z","abstract_excerpt":"The purpose of this note is to provide a family of explicit examples of $4$-dimensional operator systems contained in the Calkin algebra $\\mathcal{Q}(\\mathcal{H})$ on a separable infinite-dimensional Hilbert space $\\mathcal{H}$ for which the identity map has no unital completely positive (ucp) lift to $\\mathcal{B}(\\mathcal{H})$ with respect to the canonical quotient map $\\pi:\\mathcal{B}(\\mathcal{H}) \\to \\mathcal{Q}(\\mathcal{H})$. More specifically, to each unital $C^*$-algebra $\\mathcal{A}$ generated by $n$ unitaries and unital $*$-homomorphism $\\rho:\\mathcal{A} \\to \\mathcal{Q}(\\mathcal{H})$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00113","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.00113/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"}