Symbol n
n 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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Why this formula appears here
The middle term is the one that matters. It grows as n(n-1)/2 — quadratically in step count — while the other two terms grow only linearly. For a short loop, the quadratic term is negligible next to the fixed tax and the output cost. For a long one, it dominates completely, and no amount of shrinking or changes that; the loop’s own length has become the largest line item, all by itself.
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Published contexts (1)
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Equation 20 · AI Agents & Systems
The Economics and Physical Limits of Running AI Agents at Scale
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
The middle term is the one that matters. It grows as n(n-1)/2 — quadratically in step count — while the other two terms grow only linearly. For a short loop, the quadratic term is negligible next to the fixed tax and the output cost. For a long one, it dominates completely, and no amount of shrinking or changes that; the loop’s own length has become the largest line item, all by itself.
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