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Equation 39 · Part 3 · How Fast Can a Horizon Learn Which Path You Took?

Symbol t_c

u∈A(tc)u\in\mathcal A(t_c)
tct_c

What this part means

the become irrevocable at an intermediate cutoff.

Its job in the formula

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

Where the article explains it

It does not answer how much information has become irrevocable at an intermediate cutoff tct_c .

The passage around this formula

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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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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