Conjectural support and laminarity description for the bifurcation current

Let $\Lambda$ be the parameter space of normalized degree-$d$ polynomials $P_\lambda$, with critical points $\lambda=(c_1,\ldots,c_{d-1})$ whose product is fixed by the rotation number. Define

$$T=dd^c\bigl(\lambda\mapsto\log\operatorname{rad}(P_\lambda)\bigr),\qquad f(\lambda)=\min(|c_1|,\ldots,|c_{d-1}|).$$

Write $I_k$ for the relevant critical-boundary loci and $\operatorname{Supp}$ for support.

Conjectural support and laminarity description. Point (Q:support) holds: the support of $T$ is homeomorphic to the support of $dd^c f$. Moreover, the difference $\operatorname{Supp}T-\operatorname{Supp}(T\wedge T)=I_2-I_3$ is a finite union, over pairs $i<j$ of critical points, of $(d-2)$-dimensional topological submanifolds foliated by a one-real-parameter family of $(d-3)$-dimensional complex submanifolds, parametrized by the relative angle between the two critical points on the Siegel-disk boundary. The current $T$ is the sum over $i,j$ of the integrals, with respect to Lebesgue measure in that relative angle, of the integration currents on these manifolds. Analogous descriptions hold for $\operatorname{Supp}T^{\wedge k}-\operatorname{Supp}T^{\wedge(k+1)}$ and for $T^{\wedge k}$.

This is explicitly called a daring conjecture and is motivated by surgery from Blaschke fractions and comments of Zakeri. The preceding support question is known in the case $d=3$, but the full proposed description is not stated as resolved.