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 σf (x), the vacuum folding density. We extend this programme by proposing that the dimensionality of spacetime is itself an emergent property determined by σf. Treating the vacuum micro-state distribution as a statistical manifold, we construct the Fisher information metric gᵢjF (σf) and show that its eigenvalue spectrum defines an effective dimensionality Dₑff (σf). A self-consistency condition — the field σf 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.