This research represents a paradigmatic shift in theoretical physics by providing the first rigorous mathematical derivation of the Fine-Structure Constant (Alpha) within the Binary Holographic Topological (BHT) framework. Moving beyond empirical approximations, this work reveals the complete analytical expression of Alpha as a tripartite synthesis of the Universe Code, topological observational cost, and temporal consensus latency. The Complete Mathematical Expression of AlphaThrough the resolution of the BHT Universal Triad, the inverse of the fine-structure constant (Alpha-inverse) is derived as:Alpha-inverse = (Theta / 2) + 2pi + Delta_FBIn this identity, the Dimension-Locking Operator (Theta) is defined by the precise ratio of (8 times 10 to the 4th power) divided by (pi to the 5th power). The term 2pi is established as the mandatory topological entry fee for 3D projection, while Delta_FB (approximately 0.039) represents the impact of unobserved future blocks. Massless Black Holes and the Singularity CodeA landmark achievement of this paper is the precise calculation of the logical code for Massless Black Holes (MBHs). We define the MBH not as a gravitational collapse of matter, but as a terminal topological node characterized by the Root Privilege bitstream: (1, followed by 10 to the 122nd power minus one zeros).Physically, these entities represent pure logical anchors where the 3D mass-energy projection vanishes (M=0), while the 5D logical entropy remains strictly conserved. These MBHs serve as the final guardians of the universal boundary, locking the manifold into a self-consistent holographic shell.