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Equation 139 · The Bit Comes Back Before the Bearing

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tLt_L

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tLt_L

Symbol t_L

tLt_L 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

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What the article says around this equation

It is worth being explicit about which part of that conditional is load-bearing. Neither tLt_L nor tGt_G is arbitrary on its own — each is anchored to a cited, checkable piece of theory, and the crossover tolerance δ∗\delta^\ast is computed, not chosen after the fact to produce a headline. What is a choice, and should be named as one, is treating ϵ\epsilon and δ\delta as commensurate just because both are dimensionless numbers between zero and one. A fidelity and a normalized angular tolerance measure different things, and no law of physics says a “demanding” qubit fidelity and a “demanding” compass tolerance sit at the same point on their respective scales. The reversal at δ\delta ≈\approx…
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It is worth being explicit about which part of that conditional is load-bearing. Neither tLt_L nor tGt_G is arbitrary on its own — each is anchored to a cited, checkable piece of theory, and the crossover tolerance δ∗\delta^\ast is computed, not chosen after the fact to produce a headline. What is a choice, and should be named as one, is treating ϵ\epsilon and δ\delta as commensurate just because both are dimensionless numbers between zero and one. A fidelity and a normalized angular tolerance measure different things, and no law of physics says a “demanding” qubit fidelity and a “demanding” compass tolerance sit at the same point on their respective scales. The reversal at δ\delta ≈\approx 0.5\,rad\mathrm{rad} is not a defect in the model; it is the model correctly reporting that its own headline conclusion rests on an implicit convention about how strict is strict, a convention this article has tried to make visible rather than bury.

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