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

Building on the published finite-resolution, background-independent framework for local semiclassical gravity, this work audits its phenomenological consequences across cosmology and particle physics. The finite–continuum bridge and cosmoparticle consistency provide the organizing principles. Because the diffeomorphism-invariant Hilbert space does not factorize, the construction is formulated on a causal diamond with a boundary-completed algebra that supplies the edge data needed for a local Wheeler–DeWitt description. The operational state and semiclassical reference family then share this algebra, allowing their relative-entropy mismatch to define local dynamics as statistical inference within an entropic approach to quantum gravity. The topology-locked boundary capacity fixes an effective channel multiplicity N ≈ 1.23 × 10¹¹. Calibrating its coherent tensor fraction to Newton's constant gives a common 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. A quasi-local heat-kernel expansion maps these responses to a matching-scale effective field theory, while completely positive trace-preserving updates describe the open-modular evolution between causal diamonds. The finite–continuum bridge separates the geometric spectral response from the internal matter trace. The internal algebra \( \mathcal A_F\simeq\mathbb C\oplus\mathbb H\oplus M_3(\mathbb C) \) organizes the Standard Model structure. Once the Newton calibration, finite capacity, and internal algebra are fixed, the architecture must reproduce cosmological and microscopic targets from the same scales. In the cosmological sector, one-resolution saturation fixes the scalaron pole M_R = Mₛ and the curvature stiffness \( \lambda_{R^2}=N_{\rm eff}/12 \). The isotropic boundary response sets the coherence duration \( \mathcal N_*=18\pi \), yielding \( n_s\approx0.9646 \) and \( r\approx0.0038 \). All continuous dimensional scales cancel from the primordial scalar amplitude, leaving the pure finite-capacity relation \( A_s=81\pi/N \). Extending this same response gives exploratory late-time targets for vacuum energy, structure growth, and acceleration scale. In the cosmoparticle sector, the same capacity N and matching scale Mₛ determine the electroweak saturation limit and the gauge-coupling relations, while the scalar accessibility organizes the charged-lepton hierarchy. Finite-mesh simulations confirm the six-pole projection, attractor convergence, one-resolution matching, and the finite-\( \mathcal N \) primordial trajectory. Structural inputs, epistemic status, and failure conditions are stated explicitly. The resulting construction is usefully rigid: changing one shared input disrupts several linked relations, allowing cosmological and microscopic observables to test the same quantum-gravitational architecture.