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  <title>Claim-native multi-task regression audit</title>
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  <div class="hero"><h1>Multi-task regression: every claim measured</h1><p>Direct Algorithm 1 risks, three transfer exponents, exact low-rank balancedness, population comparability, bounded-domain logistic regression, and destructive controls.</p></div>
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    <div class="card"><div class="n">1.4098</div><p>maximum linear safety-rate ratio over 6,480 task risks</p></div>
    <div class="card"><div class="n">−1.0087</div><p>measured task-sharing exponent; theory predicts −1</p></div>
    <div class="card"><div class="n">17.23×</div><p>median logistic transfer gain over independent fitting</p></div>
    <div class="card"><div class="n">0 / 1,200</div><p>population-comparability violations</p></div>
    <div class="card"><div class="n">14,197</div><p>exact finite low-rank balancedness pairs</p></div>
    <div class="card"><div class="n">3.67e9</div><p>unsafe pooling ratio at outlier radius 100,000</p></div>
    <div class="card wide"><img src="outputs/multitask_native_audit.png" alt="Four-panel claim-native audit"></div>
    <div class="card wide small"><b>Boundary:</b> finite native-scale execution reconstructs the registered mechanisms and failure controls. The pinned source—not these finite measurements—carries the universal high-probability statements.</div>
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