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Equation 23 · Part 8 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

superscript

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

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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 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

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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