Acyclicity conjecture for the optimal-predictor graph

For $\rho$ and $n$, let $4\mathcal{G}_{\rho,n}4$ be the directed graph whose vertices are all Boolean functions of $n$ variables, with a directed edge from each function $f$ to its optimal predictor $\operatorname{sgn} T_{\rho}f$ whenever they differ; if $T_{\rho}f$ is identically zero, set $\operatorname{sgn} T_{\rho}f=f$. A cycle-free directed graph contains no directed cycles.

Optimal-predictor acyclicity conjecture. The graph $\mathcal{G}_{\rho,n}$ contains no cycles.

If true, this would make the number of $\rho$-self-predicting functions equal to the number of connected components of $\mathcal{G}_{\rho,n}$, as described in the source; the supplied text does not state a resolution.