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Equation 23 · Part 2 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

Symbol Z

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

What this part means

Z appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

Its job in the formula

Z appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

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=EZ[∏i=1npi(Z)]R=\mathbb{E}_Z\left[\prod_{i=1}^{n}p_i(Z)\right]. Running five agents against…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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