{"paper":{"title":"Layerwise Terminal Discrepancy in Chen's Reverse-Heat Coupling on the Boolean Cube","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.FA","authors_text":"Yanjin Xiang, Zhihua Zhang","submitted_at":"2026-06-03T08:09:22Z","abstract_excerpt":"We isolate a layerwise refinement of the terminal testing-discrepancy step in Chen's perturbed reverse-heat approach~\\cite{Chen2026} to Talagrand's convolution conjecture on the Boolean cube. Built on the joint-filtration martingale formulation of Chen's coupling, and on Chen's approximate monotonicity and conditional squared-score estimates being available in the joint-filtration form stated below, we prove the localized testing estimate \\[\n  D_E\\le C_\\tau\\bigl(\\cS_E+\\sqrt{\\cS_E\\,\\Pp(E)}\\bigr),\n  \\qquad E\\in\\mathcal F_\\theta, \\] where \\(D_E\\) is the localized terminal testing discrepancy and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04573","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/2606.04573/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"}