Theory of Universal Evolutive Redistribution. Universal Equation, Gravitation and Structural Signatures.

We present a unified theoretical framework, called TRUE, based on a discrete universal equation describing the accumulation, saturation and redistribution of a local constraint on a network of coupled sites. The equation is unique, explicit, local, computable in exact fractions, without eigenvalues, without continuous functions, without floating-point arithmetic. We show that it reproduces the precessions of the first 6 planets of the solar system with a maximum deviation of less than 0.05 arcsecond per century. The ratio between the corrective coefficients A and B of the force equation is derived structurally from the conductances of the network, without any free parameter. The exact conservation of flux on a three-dimensional network is verified in fractions, and the constant 1 over 4 pi follows. We finally show that the arithmetic signature of the solution depends on the valence of the network: a linear network produces Fibonacci, a binary tree produces powers of 2, a square grid produces no known integer sequence. The framework is universal in its law, local in its values.