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<p class="lead">Independent reproduction · arXiv 2507.06032v1 · OpenReview vbty65Z76C</p>
<h1>Learning-Augmented Online Covering Problems</h1>
<p>Exact finite diagnostics exercise the ICE charging mechanism, efficient-decomposition formulas, weighted set cover, and rooted Steiner reductions without presenting finite evidence as a universal proof.</p>
<section class="grid"><div class="card"><div class="n">15/15</div><div>scientific gates</div></div><div class="card"><div class="n">300</div><div>theorem-formula cells</div></div><div class="card"><div class="n">192</div><div>exact set-cover cells</div></div><div class="card"><div class="n">24</div><div>rooted Steiner certificates</div></div></section>
<img src="outputs/learning_augmented_covering_audit.png" alt="Set-cover and formula diagnostics">
<p class="scope"><strong>Scope:</strong> Theorem 5's classical <code>O(log k)</code> phrase is request-count dependence—the full source rate includes <code>log|S|</code>. Theorem 12 covers Steiner tree; the group-Steiner substitution appears separately as a general-framework application.</p>
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