The full-measure basin conjecture for the $5$-point orbit of $f_{6}$

Let $f_{6}$ be the map under discussion on ${\mathbf{CP}^{3}}$, and let the $5$-point orbit denote the orbit of the $5$-points. The basins of an attracting orbit are the sets of points whose iterates converge to that orbit. Full-measure basin conjecture. The attractor for $f_{6}$ is the $5$-point orbit, and its basins fill ${\mathbf{CP}^{3}}$ in measure. The statement is supported in the supplied text by graphical and experimental evidence for the reliability of $f_{6}$; no proof or disproof is provided.