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Equation 47 · Part 4 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

≤

∑iϵi≤ϵ.\sum_i \epsilon_i \le \epsilon.
≤

What this part means

Less than or equal to.

Its job in the formula

Less than or equal to.

The passage around this formula

For consequential work, “be careful” is not a stopping rule. Let the maximum tolerable probability of material failure be ϵ\epsilon . A conservative decomposition assigns budgets ϵi\epsilon_i to failure classes or transitions such that ∑iϵi≤ϵ\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

An inequality compares values without claiming they are equal. It describes a range, threshold, or bound that a quantity may satisfy.

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