{"paper":{"title":"Ultrapowers of spectral subspaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.OA","authors_text":"Hiroshi Ando, Isaac Goldbring","submitted_at":"2026-05-21T01:34:47Z","abstract_excerpt":"We prove, for any W$^*$-probability space $(M,\\varphi)$ where $M$ is a type $\\mathrm{III}_1$ factor, any nontrivial, proper closed $F\\subseteq \\mathbb{R}$, and any nonprincipal ultrafilter $\\mathcal{U}$ on $\\mathbb{N}$, that the ultrapower $M(\\sigma^\\varphi,F)^{\\mathcal{U}}$ of the spectral subspace $M(\\sigma^\\varphi,F)$ is a proper subset of the spectral subspace $M^{\\mathcal{U}}(\\sigma^{\\varphi^{\\mathcal{U}}},F)$. We discuss the model-theoretic implications of this result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21873","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/2605.21873/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"}