Causal Memory Gravity VI: Microscopic Origin of Inertia and Dark Energy — Controlled Mean-Field Baseline with Reduced-DPN Fluctuation Validation

Abstract

Inertia does not follow from stiffness alone: a microscopic system also needs a dynamical clock that turns restoring curvature into an oscillation or relaxation rate. Causal Memory Gravity VI uses this distinction to build a controlled mean-field baseline for effective inertia and vacuum-energy scaling in a Dynamic Planck Network (DPN). The model couples a density variable ρᵢ to a torsional phase θᵢ through Keff = Kθ + 2gρ Direct differentiation gives the exact static coupled Hessian. Gaussian integration over the torsional modes produces a thermal density shift and the effective curvature κeff(T) = κ − 2kBT [(N−1)/N] g²/(Kθ + 2gρ₀)² Its zero defines the finite-size curvature marker Tcurv(N). Because thermal fluctuations also shift the preferred density, the physical critical point must be tested at the temperature-dependent saddle with non-Gaussian corrections. The paper organizes normalization templates for Geff, ℏeff, and a vacuum-energy proxy. A periodic-lattice Langevin surrogate reproduces the expected finite-size scaling, σρ̄ ∝ N⁻⁰·⁵¹⁶±⁰·⁰²² over 64 ≤ N ≤ 1600, providing a controlled check of the mean-field approximation. The supplementary addendum separates static stiffness, dynamical normalization, and renormalization-group evolution. Once a torsional inertia is supplied, the graph spectrum determines conservative modes; matching them to the CMG memory rate additionally requires collective normalization and a causal kinetic law. The historical single-graph spectrum and RG Jacobian are retained as documented benchmarks, while the corrected positive-mass RG calculation belongs to the CMG IX interface. For the full CMG corpus, theory map, and related materials, visit: https://cmg.beogradpc.com/