This theory departs from two minimal algebraic equations—the cyclic generator $X^2 - XY + Y^2 = 0$ and the scaling generator $X^2 - XY - Y^2 = 0$—and rigorously constructs the complete mathematical skeleton of all strong-interaction structures in the universe. The two equations achieve self-consistent closure in three-dimensional space, producing the icosahedral vertex set (12 structural nodes); the tensor product of four-tier binary fission operators yields 16 dynamical nodes; their intersection on the unit sphere forms a 28-node helical-cone skeleton. Lifting this skeleton to the double cover of the binary icosahedral group $2A_5$ yields a 56-dimensional spinor propagation operator $\hat{\mathcal{T}}$. The theory contains no free parameters. Starting from these two algebraic equations, it rigorously derives the fine-structure constant, the proton-electron mass ratio, the $\pi$-$\rho$ meson mass splitting, and predicts the lightest scalar glueball mass at 1719 MeV. The provided 56x56 transition matrix allows for unconditional independent verification of all reported values.