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

What does this equation mean?

ok∼ΩH(o∣sk,qk,bk),o_k \sim \Omega_H(o\mid s_k, q_k, b_k),

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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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oko_k

Symbol o_k

oko_k 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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ΩH\Omega_H

Symbol Omega_H

OmegaHa_H 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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oo

Symbol o

o 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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sks_k

Symbol s_k

the relevant but incompletely observed repository state.

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qkq_k

Symbol q_k

the model’s query or action.

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bkb_k

Symbol b_k

a context budget.

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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

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

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Sources cited in the article section

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