No boundary repelling fixed point conjecture for the generalized filtration

Let $\mathfrak G^{(0)}=\{\mathfrak G^{(0)}_\alpha\}_{\alpha\in[\alpha_*,1]}$ be the generalized filtration, and let $f\in\mathfrak G^{(0)}_\alpha$. The function $f$ generates a semigroup of holomorphic self-maps, whose boundary repelling fixed points are understood in the usual sense. No boundary repelling fixed point conjecture. Every element $f\in\mathfrak G^{(0)}_\alpha$, for $\alpha\in[\alpha_*,1]$, generates a semigroup with no boundary repelling fixed point. The conjecture is motivated by the established absence of boundary repelling fixed points for semigroups generated by elements of the squeezing and analytic filtrations; no resolution is given here.