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Equation 23 · Part 2 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

Symbol s

Tj:(s,x)↦(s′,y,e),T_j:(s,x)\mapsto (s',y,e),
ss

What this part means

the environmental state.

Its job in the formula

s is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

with environmental state s , arguments x , resulting state s' , observation y , and error or side-effect record e .

The passage around this formula

A tool TjT_j can be represented as a partial transition function Tj:(s,x)↦(s′,y,e)T_j:(s,x)\mapsto (s',y,e). 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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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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