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Equation 1 · Part 9 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

subtraction

τ=(s0,o0,a0,s1,…,aT−1,sT),\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T),
subtraction

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

Let a task generate a trajectory τ=(s0,o0,a0,s1,…,aT−1,sT)\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T). 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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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

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