Cosmic clustering

We show that the late time hartle-hawking wave function for a free massless scalar in a fixed de sitter background encodes a sharp ultrametric structure for the standard euclidean distance on the space of field configurations. this implies a hierarchical, tree-like organization of the state space, reflecting its genesis as a branched diffusion process. an equivalent mathematical structure organizes the state space of the sherrington-kirkpatrick model of a spin glass.