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Equation 20 · A Horizon Is a Toll Booth, Not a Loophole

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⟨H(τ)⟩−E0(τ)\langle H(\tau)\rangle - E_0(\tau)

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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HH

Symbol H

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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τ\tau

Symbol τ

a time, the integral has action units.

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E0E_0

Symbol E_0

the ground-state energy of H [ 2 , 1 ].

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subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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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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How to interpret it

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What the article says around this equation

Define the object this paper needs: for a worldline Γ\Gamma traced by a processor, with instantaneous mean energy above its own ground state ⟨\langle H(τ\tau)⟩\rangle - E0(τ)E_0(\tau) measured in the processor’s own comoving rest frame at proper time τ\tau , the cumulative orthogonalization count is

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