Holographic Derivation of the Wormhole Length Distribution from Maximum Entropy in Granular Entropic Physics

This work derives the length distribution of wormhole connections in the Granular Entropic Physics (GEP) framework. We consider a network of microscopic nodes connected by wormhole-like links and analyze how these links contribute to entanglement entropy across spherical surfaces. By combining a geometric scaling argument for the flux of connections with a holographic bound on entanglement entropy, we show that the distribution must decay at least as fast as an inverse-square law. We then argue that an entropy maximization principle selects the slowest admissible decay, leading to a probability distribution proportional to 1/r². This result has direct consequences for the large-scale behavior of the network. In particular, it implies a Lévy-type distribution with exponent μ = 1 and leads to a spectral dimension ds = 6, consistent with numerical simulations. The derivation relies only on general geometric considerations and entropy constraints, making the result largely independent of microscopic details.