This article presents the Dual Architecture, an algebraic regularization method for divergent integrals in quantum field theory. The method rests on two functions defined over complementary domains: the Euler integral for the Gamma function over the positive real axis, and a companion integral over the negative real axis. When one integral representation diverges, its dual converges, and the regularized value is taken as the reciprocal of the convergent one. The sign alternation is encoded by an entire function without zeros on the negative real axis. Applied to Yang-Mills theory with gauge group SU(N), the method demonstrates the existence of a mass gap persisting to all orders of perturbation theory. The perturbative series of the Dual Architecture converges absolutely because the regularized Gamma values at negative integers decay factorially, in contrast to the factorial growth of the traditional Dyson series. Evidence for the proposal comes from two independent anomalies that the established method leaves unexplained. The first is a residual error in the WKB expansion of the quartic anharmonic oscillator, computed numerically to high order and documented in the literature. The second is the sign of the vacuum energy density, which the traditional analytic continuation yields as negative, contradicting the observed accelerated expansion of the Universe. The Dual Architecture corrects both anomalies, and they share a common origin in the same negative half-integer argument of the Gamma function. The method eliminates the renormalization scale because integrals are evaluated directly in four dimensions, producing finite values without pole subtraction. Correspondence with quantum electrodynamics at one loop is verified. The Wightman axioms are satisfied.