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Equation 40 · Part 3 · How Fast Can a Horizon Learn Which Path You Took?

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ρ0,Hu\rho^{u}_{0,H}
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What this part means

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.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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