Equation 8 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
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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Symbol g
g appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Symbol τ
τ appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Symbol P
P appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Symbol V
V appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Symbol s_T
appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →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.
How to interpret it
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What the article says around this equation
where is environmental state, the agent’s observation, and its action. Task success is not a property of the final message. It is an externally evaluated predicate V(,g) over final state and goal g . System reliability under task distribution D is . Every term matters. Change the task distribution, model, harness, tools, retry budget, permissions, environment, or evaluator and the reliability estimate changes.
Sources cited in the article section
These citations give research context. Read each source to check which claims it supports.
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