Void-Amplified Dimensional Flow (VADF): Curvature-Suppressed Anomalous Dimension and Emergent Phenomena(v.3)

We propose the Void-Amplified Dimensional Flow (VADF) model, in which spacetime dimensionality is locally modulated through a curvature-suppressed anomalous dimension η(R) ≈η∗ exp(−R/R∗), yielding spectral dimension ds(R) ≈ 4 + 2η(R). This recovers exact fourdimensional physics (ds ≈ 4) in dense/high-curvature environments, while ds ≈ 4.06–4.20emerges naturally in extremely low-curvature regimes such as cosmic voids and ultra-high vacuum (η∗ ≈ 0.03–0.10 from asymptotic safety on curved backgrounds).The preferred microscopic origin is a nonlocal realization inspired by Deser–Woodard gravity,where persistent infrared RG flow generates the curvature-dependent anomalous dimension. Themodel is consistent with precision constraints and offers falsifiable predictions testable with nearfuture experiments (2027–2032), including effects in laboratory dilute regimes (Casimir forceenhancement at large separations, modified tunneling in cold-atom traps) and cosmologicalsignatures (late-time Hubble parameter modification, suppressed growth rate fσ8, backreactionin voids with a potential self-reinforcing amplification loop).This exploratory framework provides a geometric perspective on the Hubble tension, mildS8 tension, and aspects of the cosmological constant problem without introducing new fundamental fields. Future functional renormalization group calculations on curved backgrounds mayconstrain the form more rigorously.