{"paper":{"title":"Constructing Nearby Commuting Matrices for Reducible Representations of $su(2)$ with an Application to Ogata's Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"David Herrera (Rutgers University)","submitted_at":"2022-12-12T16:19:12Z","abstract_excerpt":"Resolving a conjecture of von Neumann, Ogata's theorem in arXiv:1111.5933 showed the highly nontrivial result that arbitrarily many matrices corresponding to macroscopic observables with $N$ sites and a fixed site dimension $d$ are asymptotically nearby commuting observables as $N \\to \\infty$. In this paper, we develop a method to construct nearby commuting matrices for normalized highly reducible representations of $su(2)$ whose multiplicities of irreducible subrepresentations exhibit a certain monotonically decreasing behavior. We then provide a constructive proof of Ogata's theorem for site"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.06012","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/2212.06012/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"}