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

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V(sT,g)V(s_T,g)

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VV

Symbol V

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sTs_T

Symbol s_T

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gg

Symbol g

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subscript

subscript

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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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