Hölder continuity conjecture for core entropy of quadratic polynomials

For a quadratic polynomial, let its core entropy be the entropy of the dynamics on its Hubbard tree, and let the polynomial vary in the space of quadratic polynomials equipped with an appropriate measure. Hölder continuity conjecture. The dependence of core entropy on the polynomial is Hölder continuous, with Hölder exponent equal, up to a scaling constant, to the core entropy itself; in particular, Hölder continuity fails when core entropy is zero. This conjecture concerns the quantitative regularity of the extension of core entropy beyond postcritically finite polynomials. Continuity is known for quadratic polynomials, and partial Hölder-continuity results are known for real quadratic polynomials; the paper proves the conjectured exponent up to an arbitrarily small error for a large class of non-recurrent complex quadratic polynomials, while the full conjecture remains open.