CMG_VI_Microscopic_Origin_of_Inertia_and_Dark_Energy_in_Controlled_Mean-Field_Baseline_with_Reduced-DPN_Fluctuation_Validation

We present a controlled mean-field formulation of a microscopic Causal Memory Gravity (CMG)Hamiltonian on a Dynamic Planck Network (DPN), together with a reduced-DPN numerical fluc-tuation test that probes the large-network consistency of the mean-field baseline. The analyticalpart provides a conservative scaling framework for emergent scales associated with ℏ, G, and Λunder explicit scope restrictions. A new stochastic derivation of ℏeff from Poisson “kick” micrody-namics on the network yields a microscopic expression for the noise coefficient Dnoise and showsthat the cosmological scaling of ℏeff discriminates sharply between coarse-graining conventions: thecomoving-cell convention produces ℏeff ≈ const, consistent with observation, while the physical-Planck-cell convention predicts strong running ℏeff ∝ a−3 that is likely excluded. The numericalpart simulates a stochastic memory field on periodic lattices and finds fluctuation suppression con-sistent with central-limit scaling, σ¯ρ ∝ N −0.516±0.022 and Var(¯ρ) ∝ N −1.032±0.044, together with anapproximately size-independent stiffness proxy. These results support the internal consistency of thehomogeneous large-network regime used in the CMG mean-field program, now supplemented by anexplicit Gaussian (one-loop) determinant, an analytic CLT scaling anchor derived from the inverseHessian covariance, and formal expressions for one-loop–propagated corrections to the emergentconstants Geff and Λeff. Higher-order RG closure beyond one loop remains deferred.