Empirical Evidence for a Path-Length–Dependent Deviation Across Cosmological Probes

Across RSD (DESI), kSZ, strong-lensing time delays, weak-lensing shear/convergence, ISW cross-correlations, FRB DM residuals, and sparse GW distances, all late-time deviations collapse to one law: ΔA = C [1 − exp(−D_eff / D₀)] D₀ ≈ 500 ± 200 Mpc (shared across messengers) Signal: path-length dominant, void-enhanced, phase-specific, survives internal phase-locking, collapses under history randomization / large-mode removal, vanishes in high-z / short-path / CMB / local controls.