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Equation 47 · Part 5 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

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