  The critical height of a rational function (with algebraic coefficients) is a
natural measure of dynamical complexity, essentially an adelic analogue of the
Lyapunov exponent. Coordinate-free, it is well-defined on moduli space, but
bears no obvious relation to the arithmetic geometry of that space as a
variety. At a conference in 2010, Silverman conjectured that this disconnect is
superficial, and that in fact the critical height should be at least
commensurate to any ample Weil height on the moduli space, except on the Lattes
locus (where that has no hope of being true). Here, we prove that conjecture.
