Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Published equation contexts
Why this formula appears here
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?
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Symbol epsilon_i
epsilo is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Symbol epsilon
epsilon is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Starting index or lower bound: i
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 →How to interpret it
Read this expression 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 47 · AI Agents & Systems
Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex
This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.
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?
Equation guide → · Article →