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Fix $\Gamma$ a growth space of type $(2,2)$ and $\mathcal{E}$ and error space of rank 2. Consider $(\mu,f)$ a distributional estimation problem and $P: \Words \xrightarrow{\Gamma} \Rats$ with bounded range. $P$ is called an \emph{$\mathcal{E}^\sharp(\Gamma)$-optimal predictor for $(\mu,f)$} when for any $S: \Words \xrightarrow{\Gamma} \Rats$ with $\R_S \geq \R_P$  $$\E_{\mu^k \times U^{\R_S(k,j)}}[(P^{kj}(x,y) - f(x))S^{kj}(x,y})] \in \mathcal{E}$$  \begin{equation}  \Abs{\E_{\mu^k \times U^{\R_S(k,j)}}[(P^{kj}(x,y) - f(x))S^{kj}(x,y})]} \in \mathcal{E}  \end{equation}