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The passage around this formula

Formally, this replaces the single-loop policy with two functions and one artifact: $P = \pi_{\text{plan}}(o_0,\ g), \qquad a_t = \pi_{\text{exec}}(P,\ o_t)$. The plan P is computed against the belief state available at time zero and then held fixed; the executor applies it against a stream of later observations without necessarily invoking the planning policy again. That is precisely the assumption a classical open-loop plan makes, and it is a specific instance of the belief-state fragility decision theory already names: a policy computed once from a belief state is only as good as that belief state stays accurate, and nothing in the equation above notices when the two have quietly come apart [ 11 ] .

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