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Equation 34 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute

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P\mathcal{P}

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the prompt and decoding configuration. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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P\mathcal{P}

Symbol P

the prompt and decoding configuration.

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with weights θ\theta , reasoning effort e , prompt and decoding configuration P\mathcal{P} , evaluation harness H\mathcal{H} , serving stack S\mathcal{S} , and date t . A published number fixes s and usually reports only part of θ\theta and t . The system is underdetermined : many configurations produce the same score, and the same configuration produces different scores on different dates.

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