fraction

The passage around this formula

There is a trap. Even an orientation-blind fragment can sometimes satisfy a loose threshold by guessing from the prior. For uniform SO(3) , the probability that a blind estimate lies within geodesic angle $\epsilon$ of the true rotation is $p_{\mathrm{blind}}(\epsilon)=\frac{\epsilon-\sin\epsilon}{\pi}$. This expression follows from the Haar distribution of rotation angle, whose density on [0,$\pi$] is 2$\sin^2(\theta/2)$/$\pi$ . It passes the limiting checks: at $\epsilon$=0 , blind success is zero; at $\epsilon$=$\pi$ , it is one. The redundancy definition is informative only when 1-$\delta$>$p_{\mathrm{blind}}(\epsilon)$ . Otherwise an empty box can qualify as a witness.

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