From Planck Network to Cosmic Memory: A First-Principles Derivation of Causal Memory Gravity

We present a first-principles derivation of Causal Memory Gravity (CMG) from a microscopic Dynamic Planck Network (DPN). Spacetime is modeled as a locally finite graph of Planck-scale cells carrying torsional degrees of freedom with finite memory. We construct the graph-based Hilbert space and Hamiltonian, derive the emergence of continuum auxiliary fields in the infrared limit under explicitly stated assumptions, and integrate them out to obtain a nonlocal curvature–memory action of the form R (□ + β²)⁻¹ R. The spectral gap of the graph Laplacian determines the memory scale β, linking Planck-scale discreteness to infrared phenomenology. The resulting effective theory yields falsifiable predictions across galactic and cosmological scales, including S₈ ≈ 0.77–0.78 and the baryonic Tully–Fisher relation, while remaining compatible with stability and causality constraints.