$$s'$$

Equation 5 · Open Models

What Open Weights Actually Let You Verify

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Here $\theta$ denotes the model’s parameters and H denotes everything about the evaluation procedure that is not the model itself — the exact prompt template, the number of few-shot examples, whether a chat template is applied, how the model’s free-text output is parsed into a scored answer, and the decoding configuration. A vendor publishes one value of s . An independent lab computing its own s' is implicitly testing whether f($\theta$, H) = f($\theta$', H') , and a mismatch could in principle come from either argument.

Meanings in this article

• $s$: the vendor publishes one value of.

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Equation 13 · Open Models

What Open Weights Actually Let You Verify

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

With a closed, API-served model, both arguments are partly opaque: $\theta$ is asserted rather than shown, and $\theta$' — whatever the endpoint is actually running today — cannot be confirmed to equal $\theta$ . A reproduction attempt is chasing two unknowns with one equation. With an open-weight release, $\theta$ is a downloadable file, and a downloaded file can be checksummed against the one a vendor states it evaluated. That does not resolve the equation, but it removes a whole term from it: if the checksums match, $\theta$ = $\theta$' is no longer a hypothesis, it is a verified fact, and any gap between s and s' has to be attributed to H $\neq$ H' . That is a strictly smaller, more tractable problem…

Meanings in this article

• $s$: the any gap between.

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Equation 26 · AI Agents & Systems

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

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

with environmental state s , arguments x , resulting state s' , observation y , and error or side-effect record e . Reliability requires more than choosing the semantically correct tool. The system must construct valid arguments, detect partial execution, decide whether retry is idempotent, and represent output faithfully enough for the next decision.

Meanings in this article

• $s$: the environmental state.

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Equation 41 · AI Agents & Systems

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

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Suppose verification functions $v_1$,$\dots$,$v_m$ each observe a projection of changed state s' . Acceptance is

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