Stability of ultraviolet-cutoff quantum electrodynamics with non-relativistic matter

We prove that the quantum-mechanical ground state energy of a system consisting of an arbitrary number, M, of static nuclei of atomic number ≤ Z and of an arbitrary number, N, of Pauli electrons interacting with the quantized, ultraviolet-cutoff radiation field is bounded below by -K · M, where K is a finite constant depending on Z, on the finestructure constant α and on the ultraviolet cutoff Λ, with K ≤ K′ Λ, as Λ → ∞, and K′ independent of Λ.