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Equation 31 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

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AU(s)⊆AP(s)A_U(s)\subseteq A_P(s)

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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AUA_U

Symbol A_U

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

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ss

Symbol s

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

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APA_P

Symbol A_P

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

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subscript

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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How to interpret it

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What the article says around this equation

The distinction matters formally. Let AH(s)A_H(s) be the actions proposed by the harness, AP(s)A_P(s)⊆\subseteq AH(s)A_H(s) the actions admitted by technical policy, and AU(s)A_U(s)⊆\subseteq AP(s)A_P(s) those authorized under the approval process. Tightening approval frequency without reducing APA_P leaves a user vulnerable to habituation and mistaken consent. Tightening APA_P can prevent an action even when the model or reviewer would approve it.

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Sources cited in the article section

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