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where $\theta$ is the model’s weights, H is the harness or scaffold wrapped around it, e is the reasoning-effort or thinking-budget setting, $\tau$ is the strength of the test oracle used to grade the output, and $\phi$ is the model’s likely prior exposure to the benchmark’s specific tasks during training. A score gap between two systems is informative about $\theta$ — the thing “OpenAI versus Claude” is supposed to mean — only when H , e , $\tau$ , and $\phi$ are held fixed across both measurements. The evidence above shows that, on the leaderboards actually in public use, none of the four is reliably held fixed.

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