= Trace-power witness optimization
{title2=$\lambda_{\max}(F)^d\leq\operatorname{Tr}(F^d)\leq D\lambda_{\max}(F)^d$}
For a positive <witness acceptance operator> on dimension $D$, large trace powers approximate its largest <eigenvalue>. With an $m$-qubit <QMA> <quantum witness> and $d=2m+2$, the usual NO instances give $\operatorname{Tr}(F^d)<2^{-d}$ and YES instances give a value above $2^{-d}$. A closed product-index expansion computes the trace by recomputation with polynomial storage, avoiding logarithms and roots in a real-arithmetic implementation.
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