{"paper":{"title":"A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"David Witt Nystr\\\"om, Pietro Mesquita-Piccione","submitted_at":"2025-09-11T13:28:53Z","abstract_excerpt":"Let $X$ be a compact K\\\"ahler manifold and $\\alpha$ a K\\\"ahler class on $X$. We prove that if $(X,\\alpha)$ is uniformly K-stable for models, then there is a unique cscK metric in $\\alpha$. This was first proved in the algebraic case by Chi Li, and it strengthens a related result in an article of Mesquita-Piccione. K-stability for models is defined in terms of big test configurations, but we also give a valuative criterion as in the work of Boucksom--Jonsson together with an explicit formula for the associated $\\beta$-invariant. To accomplish this we further develop the non-Archimedean pluripot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09442","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/2509.09442/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"}