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Finally, we prove that if the weighted $\\alpha$-subharmonic measure of the compact set $K$ is H\\\"older continu"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"If the weighted α-subharmonic measure of the compact set K is Hölder continuous with respect to K, then it is Hölder continuous everywhere.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The weight function ψ is chosen so that the weighted α-subharmonic measure is well-defined and inherits the basic comparison and monotonicity properties of the unweighted α-subharmonic measure (implicit in the reduction statement when ψ ≡ -1).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Defines the weighted α-subharmonic measure and proves its continuity properties plus a characterization of (α,ψ)-regularity for compact sets.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The weighted α-subharmonic measure of a compact set K is Hölder continuous everywhere if it is Hölder continuous relative to K.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1a16f0469112bb8053e89cd4d49a5eca4cde064416b6904f3b89ddf74d274864"},"source":{"id":"2605.16851","kind":"arxiv","version":1},"verdict":{"id":"82b90c65-e064-4107-a54c-054a1321eb39","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:20:49.663610Z","strongest_claim":"If the weighted α-subharmonic measure of the compact set K is Hölder continuous with respect to K, then it is Hölder continuous everywhere.","one_line_summary":"Defines the weighted α-subharmonic measure and proves its continuity properties plus a characterization of (α,ψ)-regularity for compact sets.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The weight function ψ is chosen so that the weighted α-subharmonic measure is well-defined and inherits the basic comparison and monotonicity properties of the unweighted α-subharmonic measure (implicit in the reduction statement when ψ ≡ -1).","pith_extraction_headline":"The weighted α-subharmonic measure of a compact set K is Hölder continuous everywhere if it is Hölder continuous relative to K."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16851/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:18.985671Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:31:00.406139Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.313523Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.387415Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ced00211bb6bfa44b8e37c8c153455f3c0e989d744fd28b31aa95df57a5a8674"},"references":{"count":18,"sample":[{"doi":"","year":2021,"title":"Fundamental directions","work_id":"f8246857-4a9b-4dee-aed9-fa6a98914306","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Abdullaev B., Sadullaev A.,Potential theory in the class ofm-shfunctions.Proceedings of the Steklov Institute of Mathematics. 279 (2012), no. 1, p. 155–180","work_id":"54ef9f47-48af-4e97-ba61-4c2c98d71d2d","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Abdullaev B., Sharipov R.,Local and globalα−polar sets.Bulletin of the Institute of Mathematics. 5 (2019), p. 4–8","work_id":"6c7d4bbb-ae65-4d53-a700-fb1f5042ff8b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"Blocki Z.,Weak solutions to the complex Hessian equation.Ann. 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