Universal Hierarchy of Vortices in the Primordial Energy Waves (PEW) Framework — From Quarks to the Cosmos: One Single Mechanism

This paper (Article 13 of the PEW series) formalises the PEW VortexClosure Theorem, governing hierarchical condensation of the complexscalar field Ψ = ÷exp (iθ) from the quark scale to galaxy clusters. Main results: • Closure Theorem (N ∈ Z₂㵯): qualitative derivation of nuclear magic numbers 2, 8, 20, 28, 50, 82, 126 from the SU (2) geometry of the Hopf torus — φ⁷ ≈ 28 (3. 7%) and φ¹⁰ ≈ 126 (2. 4%) without any free parameter. • Topological Relaxation Principle: unification of all radiation forms (γ photons, UV, optical, GW) as manifestations of the same hierarchical transition mechanism. • Black Hole identified as the ontological θ → pure à frontier, characterised by R/r → ∞, θ → 0 at horizon, holographic encoding on S². • PEW cosmic cycle: cosmic expansion = à front propagation; ultimate contraction = return to Mother Wave initial condition. GW231123 (GWTC-4. 0, total mass 190–265 M☉) and the full GWTC-4. 0catalogue are analysed. Three prioritised falsifiable predictions: (PO-BH-2) BBH remnant spins → 1/φ ≈ 0. 618; (PO-GW-1) chirp mass clustering on φⁿ harmonics (KS test) ; (PO-GW-2) GW231123 correspondence with a φⁿ level of the PEW harmonic table. Bilingual FR/EN document. LaTeX sources available on request. Part of the PEW Articles series deposited on Zenodo by Michel Aldon (ORCID: 0009-0000-7215-7355) since January 2026.