Probability operator

The passage around this formula

where the components are maximum direct monetary expenditure in U.S. dollars, maximum supplied input-token context, and maximum elapsed minutes. These are intentionally not converted into one fictional currency. A system that buys more attempts, receives more context, or waits longer has changed its environment. Let Y=1 mean that an attempt reaches $A_t(x)$=1 without a predeclared collateral violation. The niche is the set $\mathcal{N}_m(B)=\left\{(g,h):\operatorname{LCB}_{0.95}\!\left[\Pr(Y=1\mid m,g,h,B)\right]\ge p^*\right\}$. where $p^*$ is a preregistered practical reliability threshold and the lower confidence bound is clustered by task, repository, and repeated attempt. The region lives in intention-gap/horizon space: g is in bit-transitions and h in active human minutes. It…

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