Equation 23 · Part 3 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

Symbol i

R=\mathbb{E}_Z\left[\prod_{i=1}^{n}p_i(Z)\right].

i

What this part means

i appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

i appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionSymbol iArticle meaning

The passage around this formula

The product formula is most misleading when failures share a cause. Let Z represent a latent condition such as an ambiguous requirement, poisoned dependency, missing platform constraint, or flawed test oracle. Conditional on Z , stages or parallel agents may appear independent; marginally, their errors are correlated: $R=\mathbb{E}_Z\left[\prod_{i=1}^{n}p_i(Z)\right]$ . Running five agents against the same incomplete specification does not create five independent opinions. They can converge on the same wrong interpretation because they share context, model family, tools, and evaluator. Even model diversity may leave the common-mode cause untouched if every run receives the same poisoned observation or passes the same weak…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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