Fractal Quantum Holographic Paradigm (FQGP)

Abstract The Fractal Quantum Holographic Paradigm (FQHP) presents a comprehensive theoretical framework in which the observed 4-dimensional Universe is a holographic projection of information encoded on a two-dimensional ontological barrier with a fractal structure. This version 2. 0 represents a fundamental revision and extension of the theory compared to version 1. 0 (December 2025). The main improvements include: A clear hierarchy of scales. A strict distinction is introduced between two key levels: the observable Universe level (space dimension d1=3, fractal dimension D1=2. 05, total number of levels Nₘax=141. 5) and the deep fractal packing level (spacetime dimension d2=4, fractal dimension D2=2. 72, number of Hilbert space levels NH=42). This resolves all contradictions associated with different fractal dimension values. A universal relation. The fundamental relation D=ΩΛ⋅d is established, linking the fractal dimension of the barrier to the embedding dimension and the dark energy fraction ΩΛ≈0. 683. This relation holds for all hierarchy levels and for arbitrary dimensions d (for instance, for d=11 it yields D≈7. 513, echoing the dimensions of string theory). Correction of key errors. All numerical calculations have been completely revised and corrected, including: the correct definition of the number of levels Nmax=ln⁡ (Robs/ℓP) ; the correction of the formula for projection angular scales, which now precisely reproduces the angle of the "axis of evil" in the cosmic microwave background (θ4=59. 4∘) ; a consistent calculation of information processing speed limits at all hierarchy levels. Cosmological predictions. Key cosmological parameters are rigorously derived from a few basic axioms and show excellent agreement with observational data (Planck 2018, DESI 2024): Scalar spectral index nₛ=0. 965; Reionization optical depth τ=0. 054; Dark energy density ΩΛ=D1/d1=0. 683 and total matter density Ωm=0. 317; Dark matter density ΩDM=0. 268 (given the observed Ωb=0. 049). Explanation of cosmological puzzles. Mechanisms are proposed for: a partial explanation of the Hubble tension (ΔH0∼1. 5−2. 0 km/s/Mpc) via local variations of the unfolding parameter η; explaining CMB anomalies (the "axis of evil, " power suppression at low multipoles, statistical anisotropy) as projections of the barrier's fractal structure. Acoustic projection theory. A detailed acoustic theory is developed, describing the propagation of information on the barrier and its transformation into observable cosmological structures (BAO, gravitational waves, anisotropy of the fine-structure constant). Experimental verification. In addition to comparisons with astrophysical data, specific protocols are presented for testing the theory's predictions on quantum processors (IBM Quantum, Google Sycamore, IonQ). Philosophical implications. The emergent nature of spacetime, the role of the observer, and the cyclic model of the Universe (the Ouroboros principle) are discussed, where information is seen as the primary substance. The work has received preliminary confirmation: analysis of the DESI void catalog indicates a fractal dimension D≈2. 06, and simulations on IBM Quantum Heron reproduce the parameter η≈0. 72 and the fractal structure. Version 2. 0 represents a coherent, mathematically rigorous, and empirically grounded theory, offering a new perspective on the fundamental structure of reality.