Exact Derivation of the Fine-Structure Constant α, Cosmological Uncertainty, and the Era of Black Hole Dominance in the Fractal Quantum Holographic Paradigm 4.0 (Preliminary version)

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 an emergent quantity determined by the geometry of the ontological barrier and the dynamics of the shift operator. A high-precision calculation of α using the fundamental constants of the theory is provided, yielding α ≈ 1/137. 036 for a refined electromagnetic level kₑm ≈ 88. 65. Fundamental limitations on accuracy due to the uncertainty of the observable universe radius Rₒbs and its evolution are discussed. It is shown that the problem of "impossibly old" galaxies (JWST) is naturally resolved in FQHP through the distinction between information time and light time. The final stage of the Ouroboros cycle — the era of black hole dominance — is described, in which rendering slows to a halt, the universe plunges into darkness, and an ontological collapse prepares the restart of the cycle.