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<!doctype html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Shuffle-aware private mean audit</title><style>body{margin:0;background:#07131d;color:#f4fbff;font:16px system-ui}.wrap{padding:28px;max-width:1100px;margin:auto}.hero{background:linear-gradient(135deg,#086a82,#563b93);padding:30px;border-radius:20px}h1{margin:0 0 10px;font-size:38px}.grid{display:grid;grid-template-columns:repeat(3,1fr);gap:14px;margin-top:18px}.card{background:#112d3d;padding:18px;border-radius:14px}.n{font-size:30px;color:#68e0cf;font-weight:800}.wide{grid-column:span 3}img{width:100%;border-radius:12px;background:white}@media(max-width:760px){.grid{grid-template-columns:1fr}.wide{grid-column:span 1}}</style></head><body><div class="wrap"><div class="hero"><h1>Shuffle-Aware Private Mean Estimation</h1><p>Exact shuffle-index formulas, PrivUnit constants, BMG asymptotics, and direct shuffled-Gaussian baseline comparisons.</p></div><div class="grid"><div class="card"><div class="n">19/19</div><p>scientific gates pass</p></div><div class="card"><div class="n">54</div><p>Monte Carlo cells</p></div><div class="card"><div class="n">π/2</div><p>PrivUnit limiting constant</p></div><div class="card wide"><img src="outputs/shuffle_mean_audit.png" alt="BMG asymptotics and mechanism comparison"></div><div class="card wide"><b>Result.</b> The BMG excess follows χ<sup>-2/3</sup>; the γ=0 shuffled-Gaussian baseline approaches the central-Gaussian floor faster. Source FFT figures remain source-reported.</div></div></div></body></html>