Published equation contexts
Why this formula appears here
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: . 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…
Read the representative guide
Symbol Z
Z appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Read this term in its guide →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
appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
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 23 · 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.
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: . 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…
Equation guide → · Article →