Equation 47 · Part 1 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

Symbol i

\sum_i \epsilon_i \le \epsilon.

i

What this part means

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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 expressionSymbol iArticle 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 $\epsilon$ . A conservative decomposition assigns budgets $\epsilon_i$ to failure classes or transitions such that $\sum_i \epsilon_i \le \epsilon$ . 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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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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