Conformal-radius bound for polynomials with an indifferent fixed point

Let $f$ be a polynomial of degree $d$ with an indifferent fixed point at the origin. Let $c_i$ be the critical points of $f$, let $\theta$ be the rotation number at the origin, and let $R(f)$ denote the conformal radius of the Siegel disk at the origin. Polynomial conformal-radius conjecture. There exists a constant $C=C(d)\in\mathbb R$ such that

$$\log R(f)\leq -\frac{Y(\theta)}{d-1}+\log\min|c_i|+C.$$

This conjecture proposes a degree-dependent extension of Yoccoz's quadratic conformal-radius estimate to arbitrary polynomials, with the nearest critical point providing the geometric scale. The supplied text gives no resolution, so its status remains open.