Evolution-Current Dynamics on an Invariant Nodal Lattice:

Abstract

We propose a preliminary kinematic framework in which physical propagation is represented as a sequence of causal transitions between nodes of an invariant underlying lattice.The lattice is assumed not to deform in response to matter; instead, matter generates an evolution-current field embedded in the invariant structure. A dimensionless local evolution state E is related phenomenologically to the magnitude u of the evolution current byE = exp−u22c2, ΦE = c2ln E = −u22.In the weak-field limit, requiring ΦE → −GM/r gives u2 → 2GM/r. For null causalpropagation we propose |v−u| = c. The outward radial branch then satisfies dr/dE = c−u, sothe critical condition u = c defines a branch-selection horizon and corresponds to EH = e−1/2rather than E = 0.A central hypothesis is that all physically realizable causal signals may propagate through the same underlying nodal-transition structure, while massive matter follows the same futurenode selection pattern subject to a timelike dynamical constraint. Light and matter are therefore treated as different dynamical sectors of one causal propagation mechanism. A233-node two-dimensional triangular lattice, representing a planar close-packed/FCC-derivednearest-neighbor structure, is included as a visualization of this hypothesis.The paper develops the kinematic framework, its weak-field limit, null propagation rule, branch-selection interpretation of gravitational bending, and the requirements for a future covariant evolution-current theory. A finite-density core is discussed conditionally: if the complete dynamics maintain finite central energy density, then m(r) ∝ r3 near the center and curvature invariants can remain finite. This paper does not claim that the completenonlinear field equations or a nonsingular black-hole solution have already been established.It defines a falsifiable research program and the calculations required to test it against generalrelativity