Symbol T_j
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A tool can be represented as a partial transition function . with environmental state s , arguments x , resulting state s' , observation y , and error or side-effect record e . Reliability requires more than choosing the semantically correct tool. The system must construct valid arguments, detect partial execution, decide whether retry is idempotent, and represent output faithfully enough for the next decision.
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Equation 23 · AI Agents & Systems
OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
A tool can be represented as a partial transition function . with environmental state s , arguments x , resulting state s' , observation y , and error or side-effect record e . Reliability requires more than choosing the semantically correct tool. The system must construct valid arguments, detect partial execution, decide whether retry is idempotent, and represent output faithfully enough for the next decision.