Symbol τ
τ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Published equation contexts
Why this formula appears here
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) :
Read the representative guide
Symbol delta
delta is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (2)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 14 · 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.
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) :
Equation guide → · Article →Equation 15 · 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.
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) :
Equation guide → · Article →