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 ∈ Z_{2^m}): 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.