Void-Amplified Dimensional Flow (VADF): Curvature-Suppressed Anomalous Dimension and Emergent Phenomena (v5 – cleaned)

This is version v5 of the preprint on Void-Amplified Dimensional Flow (VADF) model. In previous versions (v1–v4), critical inconsistencies were present in the mathematical apparatus, particularly in the derivation of the curvature-dependent anomalous dimension, fractional order implementation, graviton propagator consistency, and the nonlocal form-factor ghost-freeness arguments. In v5, the mathematical framework has been fully corrected and made internally consistent: - Rigorous derivation of η (R) = η∗ exp (−|R|/R∗) from the nonlocal condensate (Appendix C updated). - Consistent fractional d’Alembertian via spectral decomposition (no auxiliary metrics or mismatched orders). - Infrared graviton propagator and fractional Poisson equation now exactly match the heat-kernel spectral dimension ds (R) = 4 / (1 − η (R) ). - Ghost-free proof referenced to recent nonlocal gravity analyses. - Numerical values refined via toy MCMC (η∗ = 0. 055^+0. 018−₀. ₀₁₅, M ≈ (20 ± 8) H₀). - All cosmological signatures (Hubble boost ΔH₀/H₀ ≈ 7–14%, fσ₈ suppression, void lensing) now follow self-consistently from the single curvature-dependent operator. The hypothesis is now mathematically consistent and ready for further testing (laboratory Casimir/BEC + upcoming surveys Euclid/DESI). Keywords: Void-Amplified Dimensional Flow, spectral dimension flow, nonlocal gravity, Hubble tension, cosmic voids, void horizon, fractional gravity