A General Theory of Evoltropy

Evoltropy is proposed as a candidate emergent-gravity framework in which physical time is associated with the local rate of physical evolution and macroscopic spacetime geometry emerges from an underlying discrete node network. The microscopic model considered here is a three-dimensional simple-cubic network with six nearest neighbours per node. Physical propagation is local and proceeds through successive nearest-neighbour updates. The theory introduces three principal macroscopic variables: an evolution field E, a spatial network-deformation field P, and an Evolution Current J. Logarithmic variables q = ln E and s = ln P are used to formulate the continuum theory. A discrete action isproposed and its long-wavelength continuum equations are derived. In the weak-field regime, the coupled network dynamics admit the equilibrium relation s ≃ −q. This gives the effective metric ds2 = −e2qc2dt2 + e−2qdx2,and, for q ≃ Φ/c2, reproduces the standard weak-field metric of general relativity. Within this approximation the post-Newtonian parameters are γ = 1 and β = 1, so the leading predictions for gravitational redshift, light deflection, Shapiro delay, and Mercury’s perihelion advance coincide with general relativity. This agreement is explicitly restricted to the corresponding weak-field/PPN order; the nonlinear Evoltropy metric is not identical to the Schwarzschild solution. A strong-field extension introduces a non-zero-evolution condition E ≥ Emin > 0 through a saturation potential. The proposed mechanism prevents the evolution field from reaching zero at finite energy and therefore provides a candidate replacement for the classical zero-evolution/horizon-singularity limit by a high-redshift transition layer and a finite-evolution saturated core. A rigorous proof of finite curvature, the exact current back-reaction, the complete nonlinear spherical solution, gravitational radiation, cosmology, and quantum dynamics remain open problems.The paper is therefore presented as a general mathematical framework and researchprogram rather than as an established replacement for general relativity.