Published equation contexts
Why this formula appears here
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.
Read the representative guide
Symbol g
g appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Read this term in its guide →Symbol τ
τ appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Read this term in its guide →Symbol P
P appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Read this term in its guide →Symbol V
V appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Read this term in its guide →Symbol s_T
appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 8 · AI Agents & Systems
Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
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.