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Equation 2 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute

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CpreC_{\mathrm{pre}}

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pretraining compute. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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CpreC_{\mathrm{pre}}

Symbol C_pre

pretraining compute.

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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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where CpreC_{\mathrm{pre}} is pretraining compute, CpostC_{\mathrm{post}} is post-training compute, Q is the number of served requests over the system’s life, and cˉinf\bar{c}_{\mathrm{inf}} is the mean compute per request. Until roughly 2024 the third term was treated as approximately fixed for a given model, and public discussion of capability collapsed onto the first. That assumption no longer holds. On current OpenAI models, cˉinf\bar{c}_{\mathrm{inf}} is a parameter the caller sets: as verified on 8 August 2026, the model guidance documents a reasoningeg_effort control taking the values none , low , medium , high , xhigh , and max , alongside a separate text.verbosity setting [ 2 ] .

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