Fractal Quantum Holographic Paradigm (FQGP) 3.0

Fractal Quantum Holographic Paradigm (FQHP), version 3.0 This work presents the third, substantially revised version of the Fractal Quantum Holographic Paradigm (FQHP) — a coherent theoretical system in which the observed four‑dimensional Universe is a holographic projection of information encoded on a two‑dimensional ontological barrier with a fractal structure. Version 3.0 contains the following key changes and additions compared to version 2.0 (March 2026): Revised axiomatics.Axiom 3 (hierarchy of scales) has been refined: the recurrence sequence is defined as a_1 = 1, a_2 = 2, a_3 = 4, a_n = aₙ₋₁ * aₙ₋₂ for n >= 4. Axiom 6 is introduced, fixing the dimension of the Hilbert space as 2^720896. The total number of axioms is increased to six, ensuring the completeness and consistency of the theory. Rigorous mathematical justifications.Appendix A presents complete solutions to six key problems: asymptotics of the Green’s function of the fractional Laplacian on a fractal sphere, derivation of the scaling law for CMB angular scales (θ_n = θ_1 * √(a_n)), spectral derivation of the factor D/d in the trace formula (with justification of Ω_Λ = D/3), expression of the Hubble constant in terms of fundamental parameters including hierarchical amplification and IR suppression, calculation of the amplitudes A_n and the coherence factor, and numerical simulation of the transition operator Tₖₗ confirming the dominance of level n = 4 (the “axis of evil” anomaly). Refined cosmological predictions.All key parameters are derived from the axioms and agree with Planck 2018 and DESI 2024 data: spectral index n_s = 0.965, reionization optical depth τ = 0.054, densities Ω_Λ = 0.683, Ω_m = 0.317, ΩDM = 0.268 (with Ω_b = 0.049). The Hubble constant is derived as H_0 = √(λ/3) * (Ω_b / Ω_Λ) * Nₘₐₓ * (c / Robs) ≈ 79.8 km/s/Mpc, which lies within the observed range. An explanation of the Hubble tension is proposed via local fluctuations of the deployment parameter η. The “axis of evil” anomaly and the coherence factor.The angular scaling law has been corrected to θ_n = θ_1 * √(a_n) with the recurrence sequence a_n. For n = 4 we obtain θ_4 = 59.4°, which coincides with the observed CMB anomaly to within <1%. Numerical simulation of the transition operator Tₖₗ with phases modulated by the golden ratio shows that the coherence factor C(n) = |⟨v⁽ⁿ⁾ | v⁽¹⁾⟩|^2 is maximal at n = 4, explaining the dominance of this level. Revised Chapter 13.The principle of ontological identity (∝ = ∞) is formulated in a rigorous scientific style. The principle is presented as an interpretational framework that does not affect testable predictions. Experimental verification.FQHP 3.0 is supported by DESI data (fractal dimension D = 2.061 ± 0.028), quantum simulations on IBM Quantum Heron (η ≈ 0.72), and Planck data. Protocols for further tests on quantum processors, gravitational‑wave astronomy, and cosmology are proposed. The work contains 196 pages, 18 chapters, and Appendix A with mathematical justifications. Version 3.0 represents a complete, internally consistent theory that aims to describe the fundamental structure of reality, where information is the primary substance, and space, time, and gravity are emergent manifestations of its holographic projection.