HVT: Structural Dilemma of the QCD Vacuum: Why a Factorized θ Vacuum Is Cosmologically Catastrophic

This note presents a heuristic cosmological argument strongly favouring the central hypothesis of the Hidden Vacuum Topology Theory (HVT) — the non‑factorizability of the $\theta$‑vacuum partition function (T5). We analyse the observable consequences of the two alternative realisations of the QCD vacuum: the coherent, non‑factorizable T5 vacuum and the factorized ``anti‑T5'' vacuum. It is shown that the anti‑T5 scenario unavoidably generates dark‑energy density fluctuations that are 38–40 orders of magnitude above the observational limits, owing to the inevitable quantum fluctuations of the axion field during inflation. In contrast, the T5 vacuum is protected from such fluctuations because its energy density is a global, non‑local quantity. Possible escape routes (non‑smooth $f(\theta)$, absence of the axion) are examined and ruled out. A structural constraint on the source of the cosmological constant is formulated, singling out the coherent QCD $\theta$‑vacuum as the minimal known realisation. The entire construction reduces to a single falsifiable lattice prediction, making HVT a definitively testable theory. The arguments presented here are not a rigorous mathematical proof; they serve as a strong physical motivation for the T5 hypothesis and for the planned lattice test.