Regime Consistency of an Entropy-Gradient Coupling: Lyα, BAO and RSD Tests within a Structural Coherence Framework

This work evaluates regime consistency of an entropy-gradient coupling in Energy-Flow Cosmology (EFC) rather than performing a new global parameter fit. We test whether a single transition function T(z), calibrated at intermediate redshift (z ≈ 0.5) from BOSS DR12 data, produces observationally consistent behavior across three independent cosmological regimes without dataset-specific adjustments.At z = 3, where the coupling is predicted to be strongly suppressed (T ≈ 0.11), DESI Lyα P1D measurements show no significant deviation from ΛCDM, consistent with the predicted near-null effect. At z ≈ 0.4–0.6, a one-parameter background modification (β = 0.08) simultaneously improves BAO distance ratios and RSD growth-rate fits relative to ΛCDM (combined Δχ² = −3.89 on 9 data points). At recombination (z ≈ 1100), the transition function naturally approaches zero (T ≈ 10⁻¹⁰), guaranteeing effective recovery of standard gravity.We assess both EFC and ΛCDM using the Structural Coherence Evaluation (SCE) framework, which measures Layer Consistency, Model Plasticity, Explanatory Compression, Anomaly Burden, and Forbidden Pattern Coverage. EFC exhibits higher layer consistency (one mechanism spanning three regimes without patches) and lower model plasticity (decreasing effective parameter count), while ΛCDM retains greater explanatory compression within its core scope. Neither framework dominates the full SCE profile.The result is a structural consistency test, not a statistical detection of new physics. The key empirical finding is that the same coupling function produces a measured effect at z ≈ 0.5 and a consistent null effect at z = 3 without additional tuning. Further progress requires a fully self-consistent EFC background, Boltzmann-level CMB predictions, and a first-principles derivation of the coupling amplitude.