{"paper":{"title":"Fixed-Composition Shuffle Asymptotics in the Full-Support Gaussian Regime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alex Shvets","submitted_at":"2026-01-17T00:09:44Z","abstract_excerpt":"We study privacy amplification by shuffling for binary-input local randomizers with a fixed finite output alphabet and full support. For a dataset containing exactly k ones among n users, let T_{n,k} denote the shuffled histogram law. In the interior fixed-composition regime, we identify the covariance and Fisher constant governing the neighboring pair (T_{n,k},T_{n,k+1}). The correct covariance is Sigma_pi=(1-pi)Sigma_0+pi Sigma_1 rather than the multinomial covariance of the mixture. With v=W_1-W_0, the resulting constant is I_pi=v^T Sigma_pi^+ v. We prove exact likelihood-ratio identities a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.09029","kind":"arxiv","version":5},"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/2602.09029/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"}