Equation 12 · Part 6 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

subscript

R_{\mathrm{no\ recovery}}=\prod_{i=1}^{n}p_i.

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.

Full expressionsubscriptArticle meaning

The passage around this formula

Suppose a task requires n materially dependent stages. If $p_i$ is the probability stage i succeeds conditional on all prior required state being correct, then $R_{\mathrm{no\ recovery}}=\prod_{i=1}^{n}p_i$ . The equal- p simplification illustrates scale: 0.99^{100} $\approx$ 0.366 . This is not a model of real coding trajectories—the stages are correlated, checkpoints exist, and some errors are reversible—but it defeats one intuition. “Usually correct” local behavior does not imply dependable long execution.

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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.

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