{"id":"bba23258-fdb7-4602-b3d1-9d8daa9995e9","arxiv_id":"2505.14023","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For big compactified S-metrized divisors on quasi-projective varieties over adelic curves, concave transforms are constructed and shown to satisfy arithmetic volume and Hilbert-Samuel formulas.","lead":"This paper develops concave transforms for compactified S-metrized divisors on quasi-projective varieties over adelic curves, and proves an arithmetic Hilbert-Samuel formula relating their volumes to arithmetic intersection numbers. It extends Arakelov geometry tools from projective varieties and continuous metrics to singular metrics on quasi-projective spaces, with applications to equidistribution of small points.","discovery_kind":"extension","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-07T15:42:50.357569+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}