Equation 34 · Part 1 · The Economics and Physical Limits of Running AI Agents at Scale

Symbol i

i

i

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.

Full expressionSymbol iArticle meaning

The passage around this formula

That exemption changes the shape of the rate-limit exposure the same way it changed the shape of the dollar cost. In the uncached model above, step i sends (i-1) $\sigma$ tokens of retransmitted history as ordinary, fully metered input — every one of which counts against the per-minute ceiling, every single step, growing linearly with i within a single trajectory. A long, rapid, uncached loop can approach its own organization’s…

Read this part in the article →

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.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.