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These means extend the usual Kubo--Ando means of positive operators and are defined using Arveson's Radon--Nikodym theorem for completely positive maps. We prove their basic order-theoretic properties, including monotonicity, transformer and Jensen inequalities, data processing, and monotonicity with respect to the ambient map."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"Arveson's Radon-Nikodym theorem applies directly to the pairs of completely positive maps under consideration and yields a well-defined derivative that can be used to construct the means without additional restrictions."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Relative and intrinsic Kubo-Ando means are introduced for completely positive maps, satisfying order properties and reducing to prior means on matrix algebras and common domains."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Relative and intrinsic Kubo-Ando means extend operator means to completely positive maps on C*-algebras via Arveson's Radon-Nikodym theorem."}],"snapshot_sha256":"bcc226909dac90dbc794514c229290050a488699299aff3342f38dbe389eb834"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"d6c37904036a002609c8da5bb6f8fda223a76814b990415465d9f3042428a35e"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T11:39:35.526611Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T09:31:17.327218Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T08:12:54.381545Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.11701/integrity.json","findings":[],"snapshot_sha256":"c6e3def9bacbad6e7cddd40447a22a59d3ff826f73bbc54117e1b11ce10a8cb9","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a Kubo--Ando theory on order intervals of completely positive maps. Using Arveson's Radon--Nikodym theorem as a structural tool, we define relative Kubo--Ando means \\(\\Phi\\sigma_\\Omega\\Psi\\) for completely positive maps dominated by a common ambient map \\(\\Omega\\). The special choice \\(\\Omega=\\Phi+\\Psi\\) yields an intrinsic mean of two completely positive maps.\n  We prove that these means are independent of the chosen Stinespring representation and satisfy the expected order-theoretic properties, including monotonicity, transformer inequalities, Jensen-type inequalities, data proces","authors_text":"Mohsen Kian","cross_cats":["math.FA"],"headline":"Relative and intrinsic Kubo-Ando means extend operator means to completely positive maps on C*-algebras via Arveson's Radon-Nikodym theorem.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-05-12T07:58:03Z","title":"Relative Kubo-Ando Means of Completely Positive Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.11701","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-13T04:46:45.663768Z","id":"e77a508b-f9d2-411b-b10c-02b2f08d59bb","model_set":{"reader":"grok-4.3"},"one_line_summary":"Relative and intrinsic Kubo-Ando means are introduced for completely positive maps, satisfying order properties and reducing to prior means on matrix algebras and common domains.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Relative and intrinsic Kubo-Ando means extend operator means to completely positive maps on C*-algebras via Arveson's Radon-Nikodym theorem.","strongest_claim":"We introduce relative and intrinsic Kubo--Ando means for completely positive maps on C*-algebras. 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