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Published equation contexts

pblind(ϵ)=ϵ−sin⁡ϵπp_{\mathrm{blind}}(\epsilon)=\frac{\epsilon-\sin\epsilon}{\pi}

Why this formula appears here

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 ϵ\epsilon of the true rotation is pblind(ϵ)=ϵ−sin⁡ϵπp_{\mathrm{blind}}(\epsilon)=\frac{\epsilon-\sin\epsilon}{\pi}. This expression follows from the Haar distribution of rotation angle, whose density on [0,π\pi] is 2sin⁡2(θ/2)\sin^2(\theta/2)/π\pi . It passes the limiting checks: at ϵ\epsilon=0 , blind success is zero; at ϵ\epsilon=π\pi , it is one. The redundancy definition is informative only when 1-δ\delta>pblind(ϵ)p_{\mathrm{blind}}(\epsilon) . Otherwise an empty box can qualify as a witness.

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pblindp_{\mathrm{blind}}

Symbol p_blind

pbp_blind is part of the quantity the equation computes from the expression on the right.

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ϵ\epsilon

Symbol epsilon

epsilon occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

pblind(ϵ)=ϵ−sin⁡ϵπ.p_{\mathrm{blind}}(\epsilon)=\frac{\epsilon-\sin\epsilon}{\pi}.

Equation 47 · Evolutionary Physics

A Reference Frame Becomes Classical by Publishing Its Orientation

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 ϵ\epsilon of the true rotation is pblind(ϵ)=ϵ−sin⁡ϵπp_{\mathrm{blind}}(\epsilon)=\frac{\epsilon-\sin\epsilon}{\pi}. This expression follows from the Haar distribution of rotation angle, whose density on [0,π\pi] is 2sin⁡2(θ/2)\sin^2(\theta/2)/π\pi . It passes the limiting checks: at ϵ\epsilon=0 , blind success is zero; at ϵ\epsilon=π\pi , it is one. The redundancy definition is informative only when 1-δ\delta>pblind(ϵ)p_{\mathrm{blind}}(\epsilon) . Otherwise an empty box can qualify as a witness.

Meanings in this article

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