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<main class="poster" data-measure-role="poster">
  <header class="masthead" data-measure-role="header">
    <div>
      <div class="eyebrow">Independent reproduction · six registered claims</div>
      <h1>Understanding Behavior Cloning with Action Quantization</h1>
      <p class="dek">A scaled numerical audit of quantization floors, closed-loop instability, and rollout correction.</p>
    </div>
    <div class="stamp"><strong>4 · 2</strong>source exact · registered wording misstated</div>
  </header>

  <section class="body" data-measure-role="body">
    <div class="column" data-measure-role="column">
      <article class="plate" data-measure-role="card">
        <section class="claim" data-logbook-target="claim-1-behavior-cloning-with-quantized-actions-and-log-loss">
          <div class="claim-head"><span class="num">1</span><h2>Quantized estimation rate</h2></div>
          <div class="verdict">Supported · scaled audit</div>
          <p class="copy">MSE falls with sample size at slope −0.938 (R² = 0.997) before reaching the quantization floor.</p>
          <div class="visual mesh" aria-label="Bars summarizing the audited trend"><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span></div>
          <div class="control"><strong>Control:</strong> Unquantized sample means remove the floor.</div>
        </section>
        <section class="claim" data-logbook-target="claim-2-under-probabilistic-incremental-input-to-state-stability-p">
          <div class="claim-head"><span class="num">2</span><h2>Stable versus unstable rollout</h2></div>
          <div class="verdict">Supported · premise stress test</div>
          <p class="copy">Stable dynamics show polynomial-like horizon growth; ρ = 1.3 produces exponential growth with semilog slope 0.267.</p>
          <div class="visual matrix" aria-label="Matrix cells summarizing a structural certificate"><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span><span class="cell"></span></div>
          <div class="control"><strong>Control:</strong> The unstable run deliberately violates the stability premise.</div>
        </section>
      </article>
    </div>
    <div class="column" data-measure-role="column">
      <article class="plate" data-measure-role="card">
        <section class="claim" data-logbook-target="claim-3-theorem-6-shows-that-without-a-smoothness-assumption">
          <div class="claim-head"><span class="num">3</span><h2>One-step error can mislead</h2></div>
          <div class="verdict">Supported · counterexample mechanism</div>
          <p class="copy">One-step error falls from 0.72 to 0.045 as εq shrinks, while deployed regret remains fixed at 0.63 per horizon.</p>
          <div class="visual ladder" aria-label="Horizontal rungs summarizing the rate"><span class="rung"></span><span class="rung"></span><span class="rung"></span><span class="rung"></span><span class="rung"></span></div>
          <div class="control"><strong>Control:</strong> A smooth quantizer makes deployed error shrink.</div>
        </section>
        <section class="claim" data-logbook-target="claim-4-theorem-7-proves-that-model-based-data-augmentation">
          <div class="claim-head"><span class="num">4</span><h2>Rollout augmentation</h2></div>
          <div class="verdict">Misstated · registered citation or scope</div>
          <p class="copy">Auxiliary rollout correction restores linear εq scaling (slope 1.000) and reaches a 21.91× improvement at the finest grid.</p>
          <div class="visual inverse" aria-label="Descending bars summarizing the controlled comparison"><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span></div>
          <div class="control"><strong>Control:</strong> Without augmentation the deployed curve stays constant.</div>
        </section>
      </article>
    </div>
    <div class="column" data-measure-role="column">
      <article class="plate" data-measure-role="card">
        <section class="claim" data-logbook-target="claim-5-information-theoretic-lower-bounds-theorems-8-9-establish">
          <div class="claim-head"><span class="num">5</span><h2>Deterministic and stochastic rates</h2></div>
          <div class="verdict">Supported · formula audit</div>
          <p class="copy">The registered lower-bound forms cleanly separate 1/n deterministic behavior from 1/√n stochastic behavior at fixed quantization error.</p>
          <div class="visual curves" aria-label="Bars summarizing the parameter sweep"><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span></div>
          <div class="control"><strong>Control:</strong> Setting εq = 0 isolates the statistical terms.</div>
        </section>
        <section class="claim" data-logbook-target="claim-6-empirically-binning-quantizers-are-shown-to-preserve-policy">
          <div class="claim-head"><span class="num">6</span><h2>Hard-policy discontinuity</h2></div>
          <div class="verdict">Misstated · registered citation or scope</div>
          <p class="copy">Adjacent-grid TV change is 5.93e−5 for a soft binned policy but remains exactly 1 for the learned hard rule.</p>
          <div class="visual mesh" aria-label="Bars summarizing the independent audit"><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span><span class="bar"></span></div>
          <div class="control"><strong>Control:</strong> Grid refinement shrinks the soft jump, not the hard jump.</div>
        </section>
      </article>
    </div>
  </section>

  <footer class="footer" data-measure-role="footer">
    <div><strong>Scope:</strong> independent deterministic/scaled numerical audit · seed 20260726 · theorem checks do not replace proofs.</div>
    <div class="right">OpenReview 9uENnRAcSl · arXiv 2603.20538</div>
  </footer>
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