{"paper":{"title":"A Baseline $T\\log^2 T$ Upper Bound for KL-Regularized Prime--Zero Optimal Transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.NT","authors_text":"Zhejun Yang (University of Sydney)","submitted_at":"2025-09-09T01:54:30Z","abstract_excerpt":"We prove that $\\mathsf{OT}_\\eta(T)\\ll T\\log^2 T$ unconditionally via a band-limited test scheme with Fej\\'er averaging. The approach normalizes $\\|\\widehat f\\|_1=\\Theta(T^{-1})$ to ensure $\\|h\\|_1\\asymp T$ and $\\|\\widehat h\\|_1\\ll 1$, and applies an $L^1$-controlled smoothed explicit formula to bound the error terms. As a result, the prime--zero optimal transport distance admits the baseline $T\\log^2 T$ upper bound without additional assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07329","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/2509.07329/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"}