Abstract We study structural limitations of a class of geometric approaches to the Yang–Mills mass gap problem, based on the Fundamental Modular Region (FMR) with the Gribov–Zwanziger measure dµGZ = det(M[A]) e-SYM DA. This work constitutes a rigorous theory of limitations for the class under consideration, and does not claim to prove the mass gap. Rigorous results. (1) No-Go Theorem 2: under polynomial vanishing λ1(M[A]) ∼ sk, all exponential localization mechanisms based on a scalar function h(- log λ1) with h = O(√u) are forbidden. (2) Dominance Theorem 3: when multiple mode classes are present, convergence of the functional D is governed by the class with the smallest exponent βmin. (3) Explicit computation in the multiscaling regime (Section 4): with logarithmic corrections, the convergence criterion depends on the correction exponent and the spectral density. Conditional results. Under six hypotheses (Section 3): classification of spectral flow regimes and the universal survival condition 2β+p > 1; the mass gap problem reduces to three independent barriers.