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Equation 41 · How Fast Can a Horizon Learn Which Path You Took?

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ρ1,Hu\rho^{u}_{1,H}

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ρ1,Hu\rho^{u}_{1,H}

Symbol ρ^u_1,H

ρ^u1u_1,H 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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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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What the article says around this equation

Define A(tc)\mathcal A(t_c) as a preregistered set of physically admissible future protocols after the cutoff. It must specify which controls Alice retains, their duration, energy, acceleration, localization, and boundary conditions. For each u∈\inA(tc)\mathcal A(t_c) , let ρ0,Hu\rho^{u}_{0,H} and ρ1,Hu\rho^{u}_{1,H} be the completed conditional states on the declared horizon algebra. Then define an irreducible distinguishability envelope

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