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Equation 144 · The Bit Comes Back Before the Bearing

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δ≈0.5 rad\delta \approx 0.5\,\mathrm{rad}

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δ\delta

Symbol delta

delta 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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≈

≈

Approximately equal to; the equality is not exact.

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Its accuracy depends on the assumptions and range of use described in the article.

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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