Fractal Cosmogenesis: Vacuum Pressure Instability, Quantum Rebound, and √2-Recursive Primordial Fragmentation

What if the Big Bang was not a singularity but an elastic rebound from a primordial black hole — and the seeds of every galaxy were created in the fragmentation that followed? We present a comprehensive framework for cosmic origin in which the universe begins as a finite-density primordial black hole (ρcrit ≈ ρPlanck × (√2) ^−6 ≈ 10⁹³ g/cm³) that rebounds when scale-driven vacuum pressure exceeds gravitational compression. The rebound is not postulated but derived from a vacuum pressure mechanism Pᵥacᵉff = −A (L) ρ^√2 with a scale-dependent prefactor that diverges near the critical correlation scale, triggering instability through derivative comparison. The rebounding core fragments according to the √2 fractal texture, producing a discrete spectrum of primordial seeds with masses Mₙ = M₀/ (√2) ^3n. These seeds — already supermassive (10⁶–10¹⁰ M☉) — become the supermassive black holes observed at galactic centers, requiring no subsequent Eddington-limited accretion for initial formation. This resolves the JWST timing problem (SMBHs at z > 10 within ~400 Myr) and inverts the galaxy formation paradigm: galaxies form around primordial seeds, not the reverse. The framework addresses six major cosmological problems simultaneously. The initial singularity is eliminated (finite-density rebound). The horizon problem is resolved through fractal connectivity at the Planck epoch. Flatness emerges naturally from fractal expansion dynamics. CMB anomalies (low-ℓ suppression ~8%, hemispherical asymmetry) are predicted by the fractal modulation with period ln√2. The Hubble tension receives a contribution from fractal τ-field propagation corrections (~8–10% systematic offset between early and late measurements). Dark energy arises as residual vacuum pressure from incomplete rebound relaxation. Standard inflation is recovered as the mean-field limit of the fractal modulation, with the spectral index nₛ − 1 ≈ −0. 04 emerging from fractal scaling rather than slow-roll conditions, and the tensor-to-scalar ratio r ~ 10⁻³–10⁻² predicted below current upper limits. Detailed comparisons with ΛCDM, Loop Quantum Cosmology, Penrose's Conformal Cyclic Cosmology, and direct collapse models are provided, with explicit distinguishing predictions for each. All predictions are falsifiable within 5–15 years (Euclid, LISA, LiteBIRD, CMB-S4). The most distinctive test: a log-periodic modulation of the SMBH mass function with spacing (√2) ³ ≈ 2. 83 in mass ratio.