The quest to understand the origin of mass, force strengths, and other fundamental constants has long challenged theoretical physics. Traditional models typically treat these parameters as empirically fitted quantities rather than as inevitable consequences of underlying principles. In contrast, the Recognition Physics framework posits that observable phenomena emerge from the intrinsic interplay between two core postulates: dual recognition and minimal informational overhead. In this paper, we provide a rigorous derivation of the core recognition coverage function and demonstrate how the optimal “ramp–up” parameter, Xopt, emerges naturally from first principles.