The Ontological Shift Operator in the Fractal Quantum Holographic Paradigm 4.0 Explicit Form, Derivation of Constants, and Cosmological Implications (Preliminary Version)

Abstract. Within the framework of the Fractal Quantum Holographic Paradigm version 4. 0 (FQHP 4. 0), we present the explicit form of the ontological shift operator Û_φ, the fundamental generator of information dynamics on the fractal ontological barrier. Based on previ-ously established theoretical parameters—the number of fractal levels N ≈ 141. 5, the phase scaling exponent p_φ = 0. 465, and the entanglement Hamiltonian scaling expo-nent qH = −0. 4825, along with the identification of the generators with the Ricci cur-vature operator R̂ₖ—a closed mathematical form of the operator is obtained. It is shown that the overall operator scaling k^−0. 9475 naturally leads to the observed red tilt of the scalar perturbation spectrum nₛ = 0. 965 and provides a built-in mechanism for ultraviolet regularization. The connection of the operator to the effective infor-mation processing speed Vₑff and the principle of Ouroboros cyclical identity is dis-cussed.