In 1984 Poland proposed that lattice and continuum hard-core fluids are characterized by a singularity on the negative fugacity axis with an exponent, here called phi(d), that is universal, depending only on the dimensionality d. We show that this singularity can be identified with the Yang-Lee edge singularity in d dimensions, which occurs on a locus of complex chemical potential above a gas-liquid or binary fluid critical point (or in pure imaginary magnetic fields above a ferromagnetic Curie point) and, hence, with directed lattice animals in d+1 dimensions and isotropic lattice animals or branched polymers in d+2 dimensions. It follows that phi=3/2 for d greater than or equal to 6 while power series in epsilon=6-d can be derived for phi(d) and for the associated correction-to-scaling exponent theta(d) with theta(1)=1 and theta(2)=5/6. By examining the two-component primitive penetrable sphere model for d=1 and d=infinity and long series for the binary Gaussian-molecule mixture (GMM) for all d, we conclude that the universality of phi(d) and theta(d) extends to continuum fluid mixtures with hard and soft repulsive cores [the GMM having Mayer f functions of the form -exp(-r(2)/r(0)(2))]. The new estimates phi(3)=1.0877(25) and theta(3)=0.622(12) are obtained with similar results for d=4 and 5.