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1−δ>pblind(ϵ)1-\delta>p_{\mathrm{blind}}(\epsilon)

Why this formula appears here

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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δ\delta

Symbol delta

delta is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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pblindp_{\mathrm{blind}}

Symbol p_blind

pbp_blind is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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ϵ\epsilon

Symbol epsilon

epsilon is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (2)

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1−δ>pblind(ϵ)1-\delta>p_{\mathrm{blind}}(\epsilon)

Equation 52 · Evolutionary Physics

A Reference Frame Becomes Classical by Publishing Its Orientation

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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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1−δ>pblind(ϵ)1-\delta>p_{\mathrm{blind}}(\epsilon)

Equation 56 · Evolutionary Physics

A Reference Frame Becomes Classical by Publishing Its Orientation

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

subject to 1-δ\delta>pblind(ϵ)p_{\mathrm{blind}}(\epsilon) and to a fixed rule for which fragment partitions are admissible. The displayed g records the physical parameter of interest; under the Haar-average convention the resulting scalar is independent of its coordinate label. A worst-case definition would retain explicit dependence until the infimum is taken.

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