{"paper":{"title":"Uniqueness of tangent currents for positive closed currents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Tuyen Trung Truong, Viet-Anh Nguyen","submitted_at":"2025-02-10T14:56:20Z","abstract_excerpt":"Let $X$ be a complex manifold $X$ of dimension $k,$ and let $V\\subset X$ be a K\\\"ahler submanifold of dimension $l,$ and let $B\\subset V$ be a piecewise $\\mathcal{C}^2$-smooth domain. Let $T$ be a positive closed currents of bidegree $(p,p)$ in $X$ such that $T$ satisfies a mild reasonable assumption in a neighborhood of $\\partial B$ in $X$ and that the $j$-th average mean $\\nu_j(T,B,r)$ for every $j$ with $\\max(0,l-p)\\leq j\\leq\\min(l,k-p)$ converges sufficiently fast to the $j$-th generalized Lelong number $\\nu_j(T,B)$ as $r$ tends to $0$ so that $r^{-1}(\\nu_j(T, B,r)-\\nu_j( T,B))$ is locally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06532","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/2502.06532/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"}