Executive Abstract for Strategic Disclosure (Timestamp Draft) Resolving the H0 Tension with Log-Periodic Modulation of H(z) (M3E) in a Bounce-Class Symmetry Framework

Author: Mark Van Dyk Date: February 6, 2026 Keywords: H0 tension; distance ladder; CMB inference; log-periodic oscillations; BIC; cosmic chronometers; R.U.T. Abstract Late-time distance-indicator measurements continue to prefer H0 ~ 73 km s^-1 Mpc^-1, while early-time CMB-anchored LambdaCDM inference prefers H0 ~ 67-68 km s^-1 Mpc^-1 - a discrepancy widely discussed as >5 sigma, and in some recent syntheses quoted as high as ~6.5 sigma as uncertainties shrink. We propose a minimal extension to flat LambdaCDM that introduces a discrete log-periodic "ringing" signature in the expansion history, motivated by a geometric operator within the Reverse Universe Theory (R.U.T.) framework. Definition (model extension) We define M3E as a log-periodic expansion modulator acting directly on the expansion rate: H(z) = H_LambdaCDM(z) * M3E(z) M3E(z) = 1 + A * sin( Omega * ln(1+z) + phi0 ) where A 0 favors the M3E extension; under this convention we obtain DeltaBIC = +3.578. We provide a Prediction Ledger with explicit "kill switches," including: (i) a laboratory-grade entropy-bandwidth coupling test in ultra-stable timing/phase-noise metrology, and (ii) a matched-filter residual search using DESI DR2 cosmology chains/data products and high-z indicators. If these signatures are not observed at the predicted form and scale, the R.U.T. extension is falsified.