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Equation 22 · The Economics and Physical Limits of Running AI Agents at Scale

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oˉ\bar{o}

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oˉ\bar{o}

Symbol baro

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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 τ\tau or oˉ\bar{o} changes that; the loop’s own length has become the largest line item, all by itself.

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