Equation 16 · Part 7 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

subscript

o_k \sim \Omega_H(o\mid s_k, q_k, b_k),

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.

Full expressionsubscriptArticle meaning

The passage around this formula

Let $s_k$ be the relevant but incompletely observed repository state. The harness emits $o_k \sim \Omega_H(o\mid s_k, q_k, b_k)$ . where $q_k$ is the model’s query or action and $b_k$ is a context budget. Two agents using the same model can behave differently because their observation functions $\Omega_H$ expose different facts, truncate different histories, or describe tools differently.

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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.