We develop a clockwork interpretation of the Triple-Coherence Framework in which the empirical relation is interpreted as the emergent result of an internal state–holonomy–recursion architecture rather than a direct counting formula. Within this framework, the factors 2a and 3a are associated with discrete internal state sectors, (3pi)c represents a geometric transport and holonomy sector, and Ad/8 corresponds to recursive self-coupling corrections. The final radius R is interpreted as stored coherence energy analogous to the energy stored in a wound spring. We discuss structural similarities between this architecture and Quantum Chromodynamics, where color states, Wilson-loop holonomies, confinement, and gluonic self-interactions play analogous roles. The framework is further connected to the MQ-coherence formalism through the complex quantity Z. The resulting picture suggests a new interpretation of particle masses as accumulated coherence energy generated by a state–transport–recursion process. While no direct derivation from QCD is claimed, the architecture exhibits striking parallels to the mathematical structure of Yang–Mills gauge theories.