ISW Consistency Audit and Revision Patch for Energy-Flow Cosmology Cross-Correlation Predictions

This note presents a self-consistency audit of the ISW–galaxy cross-correlation predictions published for Energy-Flow Cosmology (EFC) with DESI DR1 tracers (DOI: 10.6084/m9.figshare.31301953). A fully self-consistent computation—using corrected growth-factor initial conditions, the stable f-based ISW kernel, consistent D(a) in the matter power spectrum, and both Limber and exact (non-Limber) angular projections—reveals that the originally reported bias-calibrated A_ISW values (0.56–0.15) cannot be reproduced under any physically consistent channel. Three channels are tested: (A) potential-driven (μ in the gravitational potential Φ), which produces anti-correlated ISW signal for tracers at z_eff > 0.6; (B) growth-driven (μ only in the growth ODE), which yields A_ISW ≈ 0.87–0.92 with no significant redshift dependence; and (C) covariance-weighted amplitude fitting, which does not generate the published z-trend. The note proposes minimal corrections to the ISW paper: revised A_ISW predictions (uniform ~11% suppression relative to ΛCDM), explicit channel clarification (growth-driven vs. potential-driven), removal of the cancellation metric C (not applicable under growth-driven ISW), and an updated falsification criterion. All original qualitative predictions (EFC predicts A_ISW < 1) remain valid. The revision preserves the growth equation, μ(a) parameterisation, Limber validity, and tracer definitions. Companion code is provided for full reproducibility.