Evoltropy Theory: Evolution Potential, Evolution Current, Invariant Microscopic Nodes and the Emergence of Gravitational and Relativistic Phenomena

Evoltropy Theory (ET) proposes that gravitational, relativistic, optical, and cosmologicalphenomena emerge from an underlying Evolution structure rather than spacetime curvature being the fundamental physical substrate. The framework contains microscopic nodes and their relations, a scalar Evolution state E, and a directed Evolution Current JE = EvE. The macroscopic metric is treated as a coarse-grained effective description of this deeper structure. This version develops the Mercury perihelion calculation more rigorously than the previous formulation. In particular, it introduces an explicit candidate nearest-neighbour Evolution-link transition rule and derives its continuum Painlev´e–Gullstrand-type particle action. The resulting radial first integral contains a term proportional to 2GMu3/c2; differentiation with respect to orbital angle produces the post-Newtonian term 3GMu2/c2 in the Binet equation. The coefficient 3 is therefore traced mathematically to the finite Evolution-flow contributionrather than inserted as the Schwarzschild orbital equation. The calculation remains conditional on two unresolved microscopic inputs: the invariant form of the elementary transition rule and the normalization of the gravitational Evolution flow, v^2E = 2GM/r. The latter is presently fixed by the Newtonian correspondence, while spherical node counting supplies the inverse-square scaling but not its normalization. The former is a candidate microscopic postulate and is not yet derived from a more primitive node dynamics. Consequently the Mercury result is a mathematically explicit recovery within the proposed Evoltripy construction, not yet an independent first-principles derivation of general relativity. The manuscript deliberately separates postulates, constitutive assumptions, derivations,recovery results, conjectures, and open problems. Its purpose is to establish a dated mathematical research record of the present state of the framework and to identify precisely which derivations remain necessary before submission to a peer-reviewed physics journal.