{"paper":{"title":"Globalization of local sign structures for phase-isometries on uniform algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daisuke Hirota, Izuho Matsuzaki, Takeshi Miura, Yuta Enami","submitted_at":"2026-06-21T03:29:45Z","abstract_excerpt":"We study surjective phase-isometries between the unit spheres of uniform algebras. Although such maps preserve maximal convex sets up to signs, the resulting local sign ambiguity prevents a direct application of the usual Banach--Stone type arguments for isometries. The main point of the paper is to prove that these local sign structures can be globalized on the Choquet boundary. To this end, we refine an additive Bishop-type construction and use it to propagate the sign information among the maximal convex sets associated with boundary points.\n  As a consequence, every surjective phase-isomet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22320","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/2606.22320/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"}