Equation 47 · Part 6 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex
Starting index or lower bound: i
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 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Full expression→Starting index or lower bound: i→Article meaning
The passage around this formula
For consequential work, “be careful” is not a stopping rule. Let the maximum tolerable probability of material failure be . A conservative decomposition assigns budgets to failure classes or transitions such that . This union-bound allocation can be loose, but it forces explicit questions. How much risk comes from specification ambiguity? How much from an untested platform? What is the permitted probability of credential exposure or irreversible data migration? Which observation would reduce the dominant term?
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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