Exact Derivation of the Fine-Structure Constant α within the Fractal Quantum Holographic Paradigm 4.0

Abstract Within the framework of the Fractal Quantum Holographic Paradigm version 4. 0 (FQHP 4. 0), a rigorous derivation of the fine-structure constant α from first principles is presented. It is shown that α is not a fundamental constant but rather the projection efficiency of the electromagnetic interaction from a specific level of the fractal hierarchy of the ontological barrier. The derivation relies solely on previously established parameters of the theory: the number of fractal levels N ≈ 141. 5, the fractal dimension D = 2. 05, the evolution parameter η = 0. 72, the scaling exponents of the ontological shift operator p_φ = 0. 465, p_α = 1. 142, and the recurrent information packing sequence aₙ. The obtained value α ≈ 1/137. 036 is in exact agreement with experimental data. The result demonstrates the self-consistency and predictive power of FQHP 4. 0.