Equation 16 · The Economics and Physical Limits of Running AI Agents at Scale
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Because the API is stateless between calls, step i in the loop must include, as ordinary input, everything that made it into the transcript through step i-1 : the tool results, the intermediate reasoning, the earlier outputs. Call the amount a single step permanently adds to that growing transcript — roughly plus , since both the new material a step introduces and the output it produces become part of what every later step has to resend. Without caching, step i ’s input is not just + ; it is + plus the accumulated weight of every prior step, (i-1) :
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