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Then the radius of comparison satisfies rc (A^{\\alpha}) \\leq rc (A) and rc ( C* (G, A, \\alpha) ) \\leq ( 1 / card (G) ) rc (A). The inclusion of A^{\\alpha} in A induces an isomorphism from the purely positive part of the Cuntz semigroup Cu (A^{\\alpha}) to the fixed points of the purely positive part of Cu (A), and the purely positive part of Cu ( C* (G, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.06343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-08-17T22:35:57Z","cross_cats_sorted":[],"title_canon_sha256":"9a492ec343dbb7645e0fc8d0b0a572381d27c641254537a9fa553a97700e96b6","abstract_canon_sha256":"edd0c17488198d7ee0f0fd6d2e523d8b61eb64bf0269718dd09836e87b3d9950"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:14.822916Z","signature_b64":"IVjxRTweu/LRQDuR0fg6QsUzvdZVbRRMhnsOQxhuKEenYYajCpIg23fxGVHGgCj3OzIzuAYJJJAZcHYx5CIqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cb6672fb691a594544723abcc7ebc0bbe4d4bde3dccec94b5d2d95085d3a9f4","last_reissued_at":"2026-07-04T23:58:14.822575Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:14.822575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Cuntz semigroup and the radius of comparison of the crossed product by a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"M. 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