Hidden Vacuum Topology Theory: Topological Contribution to the Vacuum Energy of Confining Gauge Theories Part 3

Starting from a minimal set of axioms capturing the nonperturbative properties of confining non-Abelian gauge theories, we prove that the vacuum of pure Yang--Mills theory necessarily contains a positive, extensive, and non-factorizable contribution to the energy density f(0)~ΛQCD⁴. We show that this topological contribution is structurally distinguished: it cannot be eliminated by any local counterterm except the identity, whose addition is equivalent to a renormalization of the bare cosmological constant, making Λeff=0 non-generic. Under minimal coupling to gravity, this contribution manifests itself as an ideal cosmological constant with $w=-1$, remaining static on cosmological scales. We further prove that in a fixed mass-independent renormalization scheme, the quantity $f(0)$ is renormalization-group invariant, dynamically fixed through the gluon condensate, and acquires the status of a physical observable. The results complete the construction of the core of the Hidden Vacuum Topology Theory (HVT) for pure Yang--Mills theory and transform the cosmological constant problem into the search for a mechanism that suppresses the structurally unavoidable contribution of order ΛQCD⁴.