{"paper":{"title":"Localized Centered Second-Chaos Operator","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangqian Zhao","submitted_at":"2026-06-24T17:42:51Z","abstract_excerpt":"We prove a localized continuous-frequency operator estimate for centered Gaussian chaoses of order two. The result applies to operator-valued centered second chaoses, including Wick-centered same-family variants, between Hilbert spaces. In the model, two Gaussian frequency legs at scale $N$, an input leg at scale $Q$, and an output leg at scale $M$ are coupled through a soft incidence kernel; non-orthogonal Gaussian profiles are represented by covariance synthesis maps.\n  The proof combines four oriented flattenings, rectangular non-commutative Khintchine inequalities, soft-incidence Schatten "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26065","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/2606.26065/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"}