A Unified Discrete Dynamics for Quantum Mechanics and Gravity: Derivation, Verification, and a Near-Term Test

The companion paper Quantum Gravity from One Axiom derived, from the single axiom of Structural Determination Theory, a discrete structure carrying a Planck-scale step measure μ = t_P/|A| whose two continuum limits are the Schrödinger equation (|A| ≫ 1) and Einstein's equation (|A| = 1). It deliberately reserved the dynamics connecting them. This paper supplies that dynamics and develops its consequences to the point of experimental test. We derive, from the action structure alone, the compatibility condition □ψ = (8πG/3)(T − 2ℒ_m)ψ that any admissibility dynamics must satisfy; show that no single-register local rule can satisfy it; and derive the unique two-register form graph-internally from counting structures the formal corpus already contains — placing the gravitational half on the same derive-then-calibrate footing as the quantum half. The resulting three-register update system (U1)–(U3′) is verified numerically in both continuum limits, including exact floor-arrival timing and attractor convergence. Realizing the matter sector as the Standard Model under the weighted coupling, an exact field redefinition decouples free fermions entirely, migrates the coupling into interactions, and — jointly with precision-gravity bounds (Cassini, lunar laser ranging, equivalence principle) — forces the coarse admissibility field to unity at all sub-Planckian densities: the realized theory is exactly general relativity plus the exact Standard Model, with black-hole entropy necessarily boundary-carried and the Hawking spectrum inherited. The theory's one near-term falsifiable prediction follows as a theorem: gravitationally-induced-entanglement experiments of the Bose-Marletto-Vedral class yield a strict null result with matter coherence surviving and no anomalous noise — a previously unoccupied position (fundamentally quantum, mediationally classical) in the live mediation debate, discriminable from graviton-mediated, collapse, postquantum, and semiclassical alternatives.