Causal Memory Gravity VII: Entropic Interpretation, Holographic Scaling, and Growth-of-Structure Constraints

This work develops the information-theoretic and observational foundations of the Causal Memory Gravity (CMG) framework. Starting from the discrete Planck-scale network, it introduces a Shannon entropy for memory degrees of freedom and shows that short-range correlations naturally lead to holographic area-law scaling consistent with black-hole thermodynamics. The memory damping parameter β is interpreted as an entropic relaxation rate, establishing a direct connection between microscopic dissipation and macroscopic gravitational behavior. The paper further derives the modified growth equation for cosmological perturbations and confronts the resulting predictions with current fσ8(z) measurements from major galaxy surveys. By linking microscopic information dynamics, emergent thermodynamics, and large-scale structure formation, this work strengthens the internal coherence of CMG and provides quantitative constraints on its phenomenological sector.