Structural Coherence Evaluation and Validation Update for Energy-Flow Cosmology in the Post-Tension Weak-Lensing Landscape

We present a Stage-III update to the observational status and methodological framing of Energy-Flow Cosmology (EFC) in light of recent weak-lensing recalibrations. Final analyses from KiDS Legacy and HSC Year 3 with DESI clustering-redshift calibration shift the late-time structure amplitude S₈ upward, reducing the previously discussed tension with CMB-inferred growth. This alters the interpretive role of EFC: rather than serving primarily as a “tension-resolution” model, it now functions as a precision structural competitor whose predictions must be evaluated through higher-order and scale-dependent observables.We introduce a Structural Coherence Evaluation (SCE) protocol that separates observation-native quantities (O-layer) from model-dependent summary statistics (M-layer). Under this framework, agreement in S₈ between models demonstrates mapping-level consistency but does not imply structural equivalence. The scientifically discriminating comparison instead operates at the observation level, where EFC predicts a modified lensing response Σ(k,z) and background-driven growth suppression through a single transition function T(z).With the background coupling fixed by BAO distances (β ≈ 0.08), EFC yields σ₈ ≈ 0.805 without post-hoc adjustment, consistent with converging Stage-III weak-lensing constraints. The focus therefore shifts to falsifiable, scale-dependent signatures in shear correlations, environment-dependent clustering, and lensing–dynamical mass comparisons. This document establishes the updated observational baseline, reframes EFC’s empirical role, and formalizes a methodology for structurally fair comparisons between cosmological models in the post-tension landscape.efc_state_vs_stageIII