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Equation 38 · Part 1 · The Economics and Physical Limits of Running AI Agents at Scale

Symbol s

ss
ss

What this part means

the number of tokens.

Its job in the formula

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

Where the article explains it

Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with m2m^2 , but the number of segments scales with n/m , so the total across the whole trajectory scales with m ⋅\cdot n — linear in n for a fixed segment length m , not quadratic.

The passage around this formula

Compaction and editing are not free, and the model above shows why they earn their keep anyway. Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with m2m^2 , but the number of segments scales with n/m , so the total across the whole trajectory scales with m ⋅\cdot n — linear in n…

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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 surrounding passage

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