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Equation 31 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute

What does this equation mean?

s=f(θ, e, P, H, S, t),s = f(\theta,\ e,\ \mathcal{P},\ \mathcal{H},\ \mathcal{S},\ t),

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Inputs and operationsf(θ, e, P, H, S, t)
Result or conditions
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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ss

Symbol s

the observed score.

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ff

Symbol f

f is an input to the expression that computes the quantity on the left.

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θ\theta

Symbol θ

the weights.

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ee

Symbol e

the reasoning effort.

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P\mathcal{P}

Symbol P

the prompt and decoding configuration.

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H\mathcal{H}

Symbol H

the evaluation harness.

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S\mathcal{S}

Symbol S

the serving stack.

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tt

Symbol t

the date.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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What the article says around this equation

Collect the moving parts and the measurement problem becomes plain. An observed score s is produced by s=f(θ, e, P, H, S, t)s = f(\theta,\ e,\ \mathcal{P},\ \mathcal{H},\ \mathcal{S},\ t). 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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