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Equation 3 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

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oto_t

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the agent’s observation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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oto_t

Symbol o_t

the agent’s observation.

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subscript

subscript

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.

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How to interpret it

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What the article says around this equation

where sts_t is environmental state, oto_t the agent’s observation, and ata_t its action. Task success is not a property of the final message. It is an externally evaluated predicate V(sTs_T,g) over final state and goal g . System reliability under task distribution D is

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