Background-Independent Semiclassical Gravity from Relative Entropy at Finite Resolution: A Phenomenological Audit

Building on a published finite-resolution, background-independent framework for local semiclassical gravity, this work examines its phenomenological consequences across cosmology and particle physics. The underlying construction is formulated on a causal diamond equipped with a boundary-completed algebra, reflecting the non-factorization of the diffeomorphism-invariant Hilbert space. This algebra supplies the edge data needed for a local Wheeler–DeWitt description and is shared by the operational state and semiclassical reference family, whose relative entropy defines the local response. The entropic boundary capacity, with its topological term set by the Euler curvature charge, fixes the channel multiplicity N ≈ 1.23 × 10¹¹. Calibrating the coherent tensor response to Newton's constant then gives the matching scale Mₛ ≈ 3.02 × 10¹³ GeV. In the equilibrium KMS regime, the leading relative-entropy Hessian separates into tensor, vector, and scalar response blocks, which a quasi-local heat-kernel expansion connects to the effective theory at the matching scale. The finite–continuum bridge uses the noncommutative-geometric algebra AF ≃ ℂ ⊕ ℍ ⊕ M₃(ℂ) with a common trace convention to map finite responses to Standard-Model observables. Once the boundary capacity, Newton calibration, and finite internal structure are fixed, the projections require no sector-specific continuous retuning. In cosmology, one-resolution saturation of the scalar-curvature response sets the scalaron pole MR = Mₛ and fixes its curvature stiffness λR² = MP²/(12Mₛ²) ≈ 5.42 × 10⁸. The isotropic boundary response gives the coherence duration N* = 18π, yielding nₛ ≈ 0.9646 and r ≈ 0.0038. All continuous scales cancel from the primordial scalar amplitude, leaving the dimensionless relation Aₛ = 81π/N ≈ 2.08 × 10⁻⁹. Extensions of the same response give exploratory late-time targets for vacuum energy, structure growth, and the acceleration scale. In particle physics, single-pixel scalar saturation provides linked electroweak consistency tests, while the vector Hessian fixes correlated gauge responses. At the matching scale the construction gives αₛ⁻¹ = 12π, αem⁻¹ = 36π, and sin²θW = 7/18. The same finite geometry carries a Lie-theoretical filtration G → g → T that selects a threefold generation carrier, whose successive accessibility levels organize the charged-lepton mass hierarchy, while canonical anticommutation relations provide the operator structure for the quark Yukawa hierarchy. Finally, finite-mesh simulations verify the main analytical mechanisms across boundary, cosmological, gauge, and flavor sectors, including modular filtration. Cross-sector consistency makes the construction usefully fragile and directly testable across correlated phenomenological projections.