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Equation 26 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

What does this equation mean?

V=1V=1

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Inputs and operations1
Result or conditionV
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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VV

Symbol V

V is part of the quantity the equation computes from the expression on the right.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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What the article says around this equation

Define C as the agent’s completion claim and V as external task success. Four states follow: V=1V=1. False completion is operationally expensive because it transfers discovery to the reviewer. It can arise from missing tests, misread output, stale state, premature stopping, or incentives in the prompt to present a polished result. A reliable harness should make “blocked,” “partially complete,” and “evidence inconclusive” legitimate terminal states.

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