Geometric-Tensegrity Analysis of the MCEC Elastic Continuum: Solution to the Yang-Mills Existence and Mass Gap Problem

This paper presents a formal solution to the Yang-Mills existence and mass gap problem through the application of the MCEC (Mass-Charge Elastic Continuum) framework. We demonstrate that by extrapolating the constitutive equations of an active elastic-tensegrity medium to subatomic scales, the non-Abelian gauge interaction undergoes an automatic algebraic scale-invariance collapse, defined as the Inertial Cancellation Principle. This cancellation redefines the energy spectrum of the quantum vacuum as a pure geometric-kinematic function. By extracting the fundamental frequency eigenvalue of the compact nuclear lattice, we analytically derive the existence of a discrete spectrum whose lowest excited state (the mass gap) is quantized at the exact value of . Finally, we derive the Geometric Projection Equation, which generates an isotropic confinement pressure of , topologically resolving QCD color confinement.