Hidden Vacuum Topology Theory: Topological Contribution to the Vacuum Energy of Confining Gauge Theories Part 1

This preprint is the first in the Hidden Vacuum Topology Theory (HVT) series — a deductive research programme, not a model-building exercise. Rather than introducing new particles, extra dimensions, or modified gravity, HVT re-examines the vacuum of established confining gauge theories (Yang–Mills, QCD) from first principles. Six minimal axioms (A1–A6) are formulated, capturing well-established non-perturbative properties: a mass gap, topological sectors, and a θ-vacuum as a coherent superposition of all sectors. From these axioms, four structural results (T1–T4) are rigorously derived. Together with Articles 2 and 3, this work forms the HVT core for pure Yang–Mills theory, addressing the origin of the cosmological constant. Crucially, the central hypothesis (T5, non-factorizability of the partition function) is falsifiable by direct lattice simulations, and a test protocol is provided. HVT core does not claim to solve the hierarchy problem; it identifies the non-eliminable QCD vacuum contribution that any consistent theory must account for.