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Equation 6 · Part 2 · What a Rule Can Bind When the System Changes Weekly

superscript

C∗C^{*}
superscript

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

Second, the meaning of a fixed number drifts, and quickly . Ho and colleagues, analysing more than two hundred language-model evaluations from 2012 to 2023, estimated that the compute required to reach a set performance threshold has halved roughly every eight months, with a 95% confidence interval of about five to fourteen months [ 19 ] . If a threshold is fixed at C∗C^{*} and efficiency improves with a halving time τ\tau , the capability reachable below the threshold grows as though the budget were expanding:

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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 surrounding passage

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