Fractal Quantum Holographic Paradigm (FQGP) 4.0

Abstract The Fractal Quantum Holographic Paradigm (FQHP) 4.0 represents the next stage in the development of a theoretical framework in which the observable four-dimensional Universe is interpreted as a holographic projection of information encoded on a two-dimensional fractal barrier. This version unifies and develops the results of previous stages (FQHP 1.0–3.0), consistently transforming the paradigm from a set of intuitive metaphors into an axiomatically constructed, dynamic, and experimentally verifiable theory, which remains open to further refinements and generalizations. Evolution of FQHP FQHP 1.0 (December 2025): The basic concepts were introduced: the ontological barrier, fractal information states N⁺ᴺ and N⁻ᴺ, the ontological shift operator F[I], the recurrent packing sequence a_n, the evolutionary parameter η, and the cyclic Ouroboros model. The Trojan–Hopfield–Zi (THZ) action was postulated. First estimates of cosmological parameters were obtained. FQHP 2.0 (March 2026): An axiomatic base was formulated, two hierarchy levels were introduced, and the universal relation D = Ω_Λ·d was established. The values Ω_Λ = 0.683, Ω_m = 0.317, n_s = 0.965, and τ = 0.054 were rigorously derived. FQHP 3.0 (April 2026): An axiom on the Hilbert space dimension dim(H_total) = 2^{720896} was added. An RG analysis was performed, yielding an anomalous dimension γ = 0.035. A two-channel structure (rendering φ and information field χ) was introduced. An acoustic theory of projection was developed, explaining the “axis of evil” (θ₄ = 59.4°) and predicting a discrete BAO spectrum. FQHP 4.0 (April 2026, the present version): A transition to a dynamic description of reality was accomplished. A unified hyperfield Φ = (φ + iχ)/√2 was introduced, and 5D and effective 3+1 Lagrangians were constructed. From the principle of maximal informational efficiency, the deep dimension D₂ = e was derived, and from a self-consistent system, the parameters η_bare = 0.719, β = 0.0345, F_chain = 0.2465 were obtained, with D₁ = 2.048 ± 0.037 predicted. The two-component nature of the unfolding parameter was established (η_grad ≈ 0.780, η_total ≈ 0.989). Dark energy is interpreted as an artifact of the time dilation of physical time, and the principle of spectral compensation explains the observed constancy of the fundamental constants. All historical numerical artifacts (such as V_max and V_eff) have been corrected and brought to a unified system of parameters: V_max = 1.01×10¹⁰⁵ op/s, V_eff = 2.56×10⁶² op/s. Experimental Verification and Predictions The analysis of DESI DR2 BAO data demonstrates that FQHP 4.0, without fitting parameters, reproduces the observational data with a quality comparable to the standard ΛCDM model, but with a drastically smaller number of degrees of freedom. Quantum simulations on IBM Quantum Heron processors have confirmed the fractal dimension D ≈ 2.05, the parameter η ≈ 0.72, and the phase coherence. Within the framework of the theory, quantitative, falsifiable predictions have been formulated for future experiments, including a discrete BAO spectrum (λ_n = λ_0 · 2^{n/2}), the stochastic gravitational-wave background BRAL-tension (f₀ = 0.573 nHz, γ = 2), and a quadratic violation of Lorentz invariance (Δc/c ∼ α₁ (E/E_P)² with α₁ = 0.048).