Equation 23 · Part 9 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex
Starting index or lower bound: i=1
What this part means
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.
Its job in the formula
i=1 appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.
Full expression→Starting index or lower bound: i=1→Article meaning
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: . 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…
Learn the underlying idea
Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.
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