Equation 10 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
the probability stage i succeeds conditional on all prior required state being correct. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol p_i
the probability stage i succeeds conditional on all prior required state being correct.
subscript
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.
How to interpret it
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What the article says around this equation
Suppose a task requires n materially dependent stages. If is the probability stage i succeeds conditional on all prior required state being correct, then
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