Equation 9 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence
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user and institutional authority. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
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.
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What the article says around this equation
where is the model policy at time t ; is the harness and its context/state machinery; is the available tool set; is the permission and sandbox policy; is the execution environment; is the collection of verification functions; and represents user and institutional authority. The time index is essential. OpenAI can update the model, CLI, documentation, or cloud runtime without changing the product name.
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