Irreversible–Action Augmented Yang–Mills Complete Constructive Proof of the Mass Gap

I present a fully constructive, parameter-free proof of the Yang–Mills mass gap for SU(Nc)in four-dimensional Euclidean space. Building on Balaban’s rigorous block–spin renormalisation group, I introduce an irreversible–action kernel which is a gauge invariant, BRST-exact,and reflection-positive modification. It is motivated by horizon thermodynamics, which suppliesuniform exponential damping in the large field sector. By combining this physical dampingwith sharp Koteck´y–Preiss and Brydges–Kennedy graph-enumeration bounds, I close the longstanding C⋆ > 1 obstacle in Balaban’s Step V, establishing a uniform cluster bound at allscales. Osterwalder–Schrader axioms remain intact, exponential clustering of Schwinger functions follows, and Nelson’s analytic-vector argument yields self-adjointness of the Hamiltonian.Finally, Glimm–Jaffe–Spencer spectral-gap estimates imply a strictly positive mass gap. Thisproof meets the Clay Institute criteria without tuning any free parameters.