σ = Em : Mass–Energy Genesis of Vacuum Information in Vacuum Folding Dynamics

The preceding paper in this series showed that the vacuum folding density σ_f is a reaction product of geometric capacity C_geo and vacuum fluctuation density F_vac. We now identify a deeper correspondence: C_geo is a mass-type quantity (the structural inertia of spacetime's information-carrying capacity, rooted in the Bekenstein bound S ≤ 2πRMc/ℏ), and F_vac is an energy-type quantity (the irreducible activation budget of quantum fluctuations). In Planck units the reactive equation σ_f = C_geo · F_vac reduces to σ = E · m, making it the information-theoretic generalisation of Einstein's E = mc². The bridge is circular: mass–energy equivalence supplies the two reactants whose product generates the information density from which gravity — and therefore mass–energy equivalence itself — emerges. Dimensionality D is the unique value at which this circular reaction is self-consistent, singling out D = 3+1 without free parameters. The complete VFD programme now reads E · m → σ_f → {G, Λ, T, D} → E = mc², closing the last conceptual gap between quantum information, emergent spacetime, and special relativity.