Analytical Fixing of the Universal Acceleration Constant α₀

This study proves that the numerical value of the universal acceleration constant $\alpha_0$, the sole fundamental scale in the "Law of Absolute Kinematics," is analytically determined by the theory, rather than relying on empirical observation. The numerical fixing of $\alpha_0$ stems from the topological constraints that enforce internal self-consistency among the four emergent physical paradigms derived in the main theory. We demonstrate that for the $\alpha_0$-geometrized spacetime to satisfy worldline statistical coherence, topological homology, and computational complexity limits, the theory is forced to admit precise discrete normalization factors. By simultaneously solving the fundamental constant relations against these internal constraints, we analytically determine the expression for $\alpha_0$: $\alpha_0 = \sqrt{\pi / (G\hbar)}$. This theoretically calculated value exhibits high-precision concordance with high-energy physics and cosmological observations, elevating $\alpha_0$ from an observable parameter to an analytic invariant of the unified theory.