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Equation 27 · Part 1 · The Economics and Physical Limits of Running AI Agents at Scale

Symbol i

ii
ii

What this part means

i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

A retry is not a second, independent request. It is the same step, re-attempted, and because a step’s cost is cic_i — a function of how much history has already accumulated by step i — a retry at step one hundred costs roughly as much as step one hundred did the first time, not as much as step one. This is easy to miss if retries are budgeted as a flat percentage overhead on an average request cost, because the average request in a long loop is far cheaper than a late one.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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