Void-Amplified Dimensional Flow (VADF): Curvature-Suppressed Anomalous Dimension and Emergent Phenomena(v.4)

We propose the Void-Amplified Dimensional Flow (VADF) model, in which spacetime dimensionality is locally modulated through a curvature-suppressed anomalous dimensionη(R) ≈ η∗1 − exp(−R/R∗).This form emerges from the competition between the Seeley–deWitt coefficient ˜ a2 ∝ R (screeningexcess dimensionality in high-curvature regions) and bi-metric splitting (activating mild infraredexcess in low-curvature regimes). The spectral dimension readsds(R) ≈ 4 + 2η(R),recovering ds ≈ 4 in dense regions while ds ≈ 4.06–4.20 emerges in cosmic voids (η∗ ≈ 0.03–0.10).The microscopic origin is a nonlocal bi-metric realization inspired by Deser–Woodard gravity.The modified infrared propagator G(p) ∼ 1/(p2 − m2)1−η(R)/2 underlies Casimir enhancement,fractional tunneling in cold atoms, and cosmological signatures: Hubble boost ∆H0/H0 ≈ 5–7 %,suppressed fσ8, and enhanced void lensing ∆κ/κ ≈ 0.18–0.25. All arise from a self-reinforcingamplification loop driven by the fractional Poisson equation ∇2+ϵ(R)Φ = 4πGρ.The model introduces the concept of a void horizon — the inverse of black-hole event horizons — where minimal curvature amplifies vacuum fluctuations and weakens classical causality.This geometric framework addresses the Hubble tension, mild S8 tension, and aspects of thecosmological constant problem without new fields.Keywords: Void-Amplified Dimensional Flow, spectral dimension, nonlocal gravity, Hubbletension, Casimir effect, cosmic voids, void horizon. Cleaned and refined version (13 pages). Earlier intermediate versions are available as separate records.