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π\pi

This entry links every published equation using this exact notation. Its meaning may change between equations.

Meanings in context

Used in 47 equations

CAI(π)=1N∑i=1N1[trial i converges on the recolored true target, not the red decoy, within the paper’s own 2-meter success radius].\mathrm{CAI}(\pi) = \frac{1}{N}\sum_{i=1}^{N} \mathbb{1}\left[\text{trial } i \text{ converges on the recolored true target, not the red decoy, within the paper's own 2-meter success radius}\right] .

Every Test Changed the Scene and Kept the Chair Red · Equation 6

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

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∣ddτln⁡ ⁣[⟨H(τ)⟩−E0(τ)]∣≪2[⟨H(τ)⟩−E0(τ)]πℏ.\left|\frac{d}{d\tau}\ln\!\left[\langle H(\tau)\rangle - E_0(\tau)\right]\right| \ll \frac{2\left[\langle H(\tau)\rangle-E_0(\tau)\right]}{\pi\hbar}.

A Horizon Is a Toll Booth, Not a Loophole · Equation 37

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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N⊥=2πℏE∞ Δt=2πℏ(f E0′)Δτf=2πℏE0′ Δτ.N_\perp = \frac{2}{\pi\hbar}E_\infty\,\Delta t = \frac{2}{\pi\hbar}\left(\sqrt f\,E_0'\right)\frac{\Delta\tau}{\sqrt f} = \frac{2}{\pi\hbar}E_0'\,\Delta\tau.

A Horizon Is a Toll Booth, Not a Loophole · Equation 52

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

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