Hidden Vacuum Topology Theory: Topological Contribution to the Vacuum Energy of Confining Gauge Theories Part 2

This preprint is the second article in the Hidden Vacuum Topology Theory (HVT) series. It proves the central hypothesis T5: in pure Yang–Mills theory with confinement and a mass gap, the logarithm of the θ-vacuum partition function contains an extensive, positive contribution that cannot be represented as a sum of independent contributions from topological sectors. The proof employs a rate function built via the large deviation principle and a saddle-point method. This establishes the non-additive (coherent) nature of the vacuum energy density f(0) and fixes it as a renormalization-group invariant quantity of order ΛQCD⁴. The CPN-1 model serves as an exactly solvable illustration, and a concrete lattice measurement protocol is provided. The results form the basis for Article 3, where it is shown that this contribution cannot be eliminated by local counterterms and thus manifests as an effective cosmological constant. Crucially, HVT makes a falsifiable prediction: the difference Δ(V) = ln Z(0,V) - ∑Q ln ZQ(V) grows super-extensively, e.g., as V3/2 in the Gaussian case, which can be tested with present-day supercomputers.