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    <div style="font-size:22px;font-weight:700;">Steady-State Behavior of Constant-Stepsize Stochastic Approximation</div>
    <div style="opacity:.85;margin-top:4px;">ICML 2026 reproduction (CPU-only) - all 6 claims verified</div>
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      <b>Claim 1 - W<sub>1</sub> &le; U&radic;&alpha; log(1/&alpha;)</b><br>bound ratio decreasing for SGD / linear / contractive / Markov SA.
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      <b>Claim 2 - SGD smooth-SC (Prop 3.1)</b><br>W<sub>1</sub> slope 0.533 (theory 0.5+log), R&sup2; 0.998.
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      <b>Claim 3 - linear &amp; contractive SA</b><br>slope 0.561 / 0.512; S<sub>Y</sub> matches Lyapunov eq to 3 dp.
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      <b>Claim 4 - Berry-Esseen tail</b><br>sup<sub>a</sub> a|&Delta;| &prop; &alpha;<sup>0.58</sup> (theory &frac14;+log<sup>&frac12;</sup>).
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      <b>Claim 5 - Markovian noise</b><br>floors vs naive G (0.09); vanishes vs corrected G.
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      <b>Claim 6 - Gibbs limit for |x|<sup>h</sup></b><br>&alpha;<sup>0.513</sup> (h=2), &alpha;<sup>0.249</sup> (h=4); kurtosis 2.19.
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    NumPy/SciPy simulation - arXiv:2602.13960 - OpenReview m4TAzup6Yc
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