The ACORN Completion: A Single 5D Curvature Engine Underlying Mass, Charge, Relativity, Gravity, Electromagnetism, and Quantum Action

We present the geometric completion of Newton’s law of motion, demonstrating that inertia, charge, gravity, electromagnetism, quantum action, the speed of light, and theStandard Model interaction structure all emerge from a single two-channel curvature engine in five-dimensional (5D) Spacetime+. This engine, the ACORN (Alternating Curvature Oscillation Relation), describes each particle through a hyperbolic curvature phasor with two components: an even curvature channel m′ (inertial–gravitational), and an odd curvature channel q ′(electromagnetic). In the neutral limit the ACORN reduces to Newton’s law; under projection, its hyperbolic structure produces Einstein’s special relativity; summed incoherently, the even channel produces Newtonian gravity; summed coherently, the odd channel produces Coulomb’s law; and its internal periodicity yields Planck’s constant. The fine structure constant arises as the ratio q′/m′ , while the gravitational and Coulomb couplingsemerge as even- and odd-channel curvature couplings, respectively. This framework reduces all forces to projections of curvature, obtaining gravitational, electromagnetic, weak, and strong interactions as manifestations of the same underlying geometric object. The ACORN structure therefore constitutes a minimal and complete geometric unification of all known physics.