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  "path": "/abs/2605.13771v1",
  "publishedAt": "2026-05-14T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Christopher Williamson"
  ],
  "textContent": "**Authors:** Christopher Williamson\n\nA pair of probability distributions over $\\\\{0,1\\\\}^n$ is said to be $(k,δ)$-wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $δ$. Previous works introduced this concept and study when and how well one can distinguish between such a pair of symmetric distributions by observing $t$ bits. We use a simple hypergeometric smoothing approach and Hahn polynomials to obtain new upper bounds that apply across a wider range of parameters and improve previously available bounds in several regimes. In particular, prior works left open the basic question of whether there exist constants $0",
  "title": "Upper Bounds for Symmetric Approximate Bounded Indistinguishability"
}