Weak boundedness theorems for canonically fibered Gorenstein minimal 3-folds

Let X be a Gorenstein minimal projective 3-fold with at worst locally factorial terminal singularities. Suppose the canonical map is of fiber type. Denote by F a smooth model of a generic irreducible element in fibers of phi(1), and so F is a curve or a smooth surface. The main result is that there is a computable constant K independent of X such that g(F) less than or equal to 647 or p(g)(F) less than or equal to 38 whenever p(g)(X) greater than or equal to K.