The full-measure basin conjecture for the $20$-point orbit of $h_{11}$

Let $h_{11}$ be the map under discussion on ${\mathbf{CP}^{3}}$, and let the $20$-point orbit denote the orbit of the octahedral $20$-points. A basin is the set of points whose iterates are attracted to this orbit. Full-measure basin conjecture. The $20$-point orbit is the attractor for $h_{11}$, and the corresponding basins have full measure in ${\mathbf{CP}^{3}}$. This claim is presented as an experimental dynamical assertion about the global attraction of $h_{11}$; the supplied text gives no resolution beyond the reported numerical evidence.