The Gravitational Memory Principle: Why Spacetime Cannot Be Markovian in an Entropy-Bounded Universe

Physical Context: General Relativity supplies local geometric constraints but does not determine a constitutive closure for the vacuum sector. Standard practice assumes a Markovian (time-local) closure. However, in an entropy-bounded universe, a cosmological horizon introduces a traced-over sector with finite information capacity and a correlation time τcorr that tracks the background evolution time τdyn. In the absence of the controlling hierarchy τcorr≪τdyn, a time-local closure is not parametrically controlled. A retarded (non-Markovian) constitutive sector emerges as the generic effective structure after coarse-graining. Structural Architecture: this manuscript establishes the Gravitational Memory Principle, providing a foundational architecture for horizon coarse-graining. Rather than treating vacuum energy as a bulk ultraviolet anomaly, the framework models it as a boundary infrared response. The coupling efficiency across the causal boundary is defined by a dimensionless equilibrium admittance, η0. Under causality, passivity, and reflectionless matching of complementary Stinespring channels, the admittance is constrained to η0=1/(2π). This structural value is independently corroborated by horizon KMS periodicity and algebraic modular theory. Benchmark Predictions: under a maximum-entropy criterion, the minimal causal kernel governing the retarded response is exponential. Adopting a declared Euclidean normalisation scheme for the static patch, the framework yields a parameter-free benchmark prediction for the late-time vacuum fraction: ΩΛ,0=2π/9≃0.698. Scope and Multiscale Framework: this document serves as the foundational "Hub" of the framework. It establishes the scale-independent structural constants without adjusting parameters to fit cosmological datasets. The framework provides a multiscale architecture where the identical interface constant η0 governs cosmological "thawing" acceleration (w0≃−0.92), galactic history-dependent response, and ultraviolet bandwidth diagnostics under scale-specific forcing. Phenomenological data pipelines (such as DESI BAO validation) are logically separated and addressed in companion manuscripts.