Scale-Dependent Dimensionality with Local Screening and Emergent Phenomena (v2)

We propose that spacetime dimensionality is locally modulated through a density-dependentspectral dimension ds(ρ) ≈ 4 + δ(ρ), where δ(ρ) ≈ 2(γ(ρ) − 1) and γ(x, t) is a single dynamicalparameter screened to ≈ 1 in high-density regions. This yields ds ≈ 4 (recovering standard quantummechanics and general relativity) in dense environments, and ds ≈ 4.1 (effective dimensionalitydeff ≈ 4.1, weakened gravity, emergent dark energy) in extremely low-density regimes such ascosmic voids and ultra-high vacuum.The framework is implemented via a density-dependent measure v(ρel) in the action, leading tomodified Friedmann equations and variable-order fractional quantum mechanics in dilute systems.A microscopic origin is proposed within the Asymptotic Safety program, where density modulates the infrared RG flow, allowing persistent quasi-marginal anomalous dimension in low-densityregimes. The model is consistent with precision constraints and offers falsifiable predictions, including Casimir force enhancement at large separations due to excess vacuum modes, modifiedtunneling in dilute cold-atom traps, and CMB lensing/ISW signatures in voids, testable with nearfuture experiments.