Symbol R_no recovery
o recovery is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
Suppose a task requires n materially dependent stages. If is the probability stage i succeeds conditional on all prior required state being correct, then . The equal- p simplification illustrates scale: 0.99^{100}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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Symbol i
i appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol n
n appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol p_i
the probability stage i succeeds conditional on all prior required state being correct.
Read this term in its guide →Starting index or lower bound: i=1
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Read this term in its guide →Ending index or upper bound: n
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 12 · AI Agents & Systems
Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Suppose a task requires n materially dependent stages. If is the probability stage i succeeds conditional on all prior required state being correct, then . The equal- p simplification illustrates scale: 0.99^{100}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.