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Equation 23 · Part 6 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.