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Equation 23 · Part 7 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

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