Dimensional Coupling in Vacuum Folding Dynamics: Information Density as the Origin of Spacetime Dimensionality

Within the Vacuum Folding Dynamics (VFD) framework, the gravitational constant G and the cosmological constant Λ emerge as functions of a single scalar field σ_f(x), the vacuum folding density. We extend this programme by proposing that the dimensionality of spacetime is itself an emergent property determined by σ_f. Treating the vacuum micro-state distribution as a statistical manifold, we construct the Fisher information metric g_ij^F(σ_f) and show that its eigenvalue spectrum defines an effective dimensionality D_eff(σ_f). A self-consistency condition — the field σ_f must inhabit the spacetime whose dimensionality it generates — yields a fixed-point equation whose unique stable solution is D = 3+1. We show that the Landau–Ginzburg barrier in the VFD potential acquires a D-dependent prefactor a(D) = (D−1)/(2D), providing a concrete mechanism for dimensional selection. Connections to causal dynamical triangulations, the holographic principle, and Wheeler's "it from bit" are discussed.