Relative-Entropy Variational Principle for Semiclassical Gravity with Finite-Resolution Boundaries

We propose a causal-diamond formulation of semiclassical gravity in which a finite-resolution boundary regulator (“Coherency Screen”) supplies the edge structure for a local Wheeler–DeWitt description. Dynamics are defined by an informational principle: for each diamond O, the action is the relative entropy Sᵣel (ρO ∥ σOλ) between the physical state and a reference family on a fixed algebra. In the modular/KMS regime, the vacuum is at entanglement equilibrium; the leading dynamics become a linear-response problem governed by the Hessian of relative entropy (the Kubo–Mori metric). This Hessian organizes deformations into tensor, vector, and scalar sectors, yielding Einstein stiffness, Yang–Mills susceptibilities, and mass gaps. The resulting local EFT is organized by a heat-kernel expansion (identifying the leading R² operator) and is compatible with a spinorial transport structure. Edge-mode counting and Newton’s constant G fix the resolution scale Mₛ ≈ 3 × 10¹3 GeV. Identifying Mₛ with stiffness saturation places the high-curvature regime in a plateau universality class, predicting a tensor-to-scalar ratio r ≈ 10^−3. We further discuss how this boundary logic constrains gauge and mass sectors, suggesting discrete coupling relations and a geometric hierarchy for charged leptons. Finally, we outline late-time phenomenology in which finite resolution induces stiffness running and horizon-set acceleration. The construction yields correlated, falsifiable targets tied to a single scale.