Fractal Quantum Holographic Paradigm (FQGP) 5.0

Modern theoretical physics has reached a plateau: the Standard Model and General Relativity, underpinned by the ΛCDM cosmological paradigm, encounter intractable conceptual discontinuities — from the nature of dark matter and dark energy to the problem of singularities. The present work constitutes the fifth iteration of the Fractal Quantum Holographic Paradigm (FQHP 5. 0), which synthesises and reinterprets its predecessors, transforming from a descriptive theory into a rigorous mathematical platform that unifies quantum gravity, hydrodynamics, and cosmology. FQHP 5. 0 elevates the χ-regularisation mechanism to the rank of a single Universal Principle: reality is not destroyed by singularities, but employs them as the engine of evolution. Observable spacetime (the φ-channel) possesses an inbuilt safety valve — a drain of excess energy into the informational χ-space via a fractal interface of dimension 1. 048 Key results of the work: Solution of a Millennium Problem: The global regularity of the fractal Navier–Stokes equations is proved (through a transition into the subcritical Sobolev regime at β = 1. 048). Singularities are prevented by a displacement of excess information along the 5D y_χ-axis. An Ontology of Mass and Velocities: Mass is interpreted as a measure of rendering density, and the speed of light c as a hardware limitation on the throughput of the barrier. Dark energy is reinterpreted as an artefact of the dilation of physical time (dtINSIDE = √ (1 - ηₜotal) ⋅ dtABOVE). Experimental Confirmation on IBM Quantum: On the ibmfez processor, the existence of φ→χ conversion has been experimentally confirmed (the anomalous P (0) < 0. 5 deficit in SWAP tests, impossible in standard QM). The conversion efficiency reaches 33% for the fractal dimension D=2. 05. Astrophysical Predictions: A resonance of the χ-channel in the soft X-ray range (λᵣes = 2. 6 nm) is rigorously derived, and a new component of the stochastic gravitational-wave background is predicted — BRAL tension (with a threshold frequency f₀ = 0. 573 nHz and spectral index γ = 2). Cyclic Cosmology: The closure of the Ouroboros cycle is ensured by the unitary Last Turn operator Ŵ, which preserves topological invariants and the structure constants of Lie algebras, rendering the end of the Universe an asymptotically unreachable horizon (the "eternal present") for an internal observer. The work rests upon the rigorous mathematical apparatus of Caputo fractional derivatives, Sobolev function spaces, the THZ hyperfield Lagrangian, and category theory.