{"paper":{"title":"A Cohesive $\\infty$-Topos with a Quantum Modality from Finite-Dimensional $C^{*}$-Algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.CT","authors_text":"Joey Woo","submitted_at":"2026-06-01T13:56:27Z","abstract_excerpt":"We construct a cohesive $\\infty$-topos $\\mathbf{H}_{\\mathbb{Q}}$ equipped with a \\emph{quantum modality} -- an idempotent product-preserving comonad $Q^{\\diamond}$ with right adjoint $Q_{\\bullet}$ satisfying the Beck--Chevalley compatibility conditions with the cohesive structure $(\\Pi,\\flat,\\sharp)$. The model is the functor $\\infty$-topos $\\operatorname{Fun}(\\mathbf{C}^{*}\\mathbf{Alg}_{\\mathrm{fd}},\\; \\mathbf{H}_{\\mathrm{sm}})$, where $\\mathbf{H}_{\\mathrm{sm}}$ is the smooth cohesive $\\infty$-topos and $\\mathbf{C}^{*}\\mathbf{Alg}_{\\mathrm{fd}}$ is the category of finite-dimensional $C^{*}$-a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02269","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/2606.02269/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"}