PEW Framework — Technical Note: Topological Relaxation of Free Neutrons — A Geometric Mechanism for the Neutron Lifetime Puzzle

The PEW (Primordial Energy Waves) framework models all particles as topologicalHopf vortex configurations of a single complex scalar field Ψ = ÷exp (iθ). Within this framework, the neutron is a stable three-quark Hopf vortex admittingharmonic excitation modes of the phase field θ. We show that freshly producedfree neutrons naturally retain such excited modes (δθₙ, n ≥ 1) which relaxelectromagnetically on a timescale τ_γ of order seconds to tens of seconds. Beam neutrons are measured before full relaxation (higher topological barrier →slower β-decay), while bottle neutrons have relaxed to the ground state (lowerbarrier → faster β-decay). This provides a parameter-free geometric mechanismfor the ~10 s beam/bottle discrepancy, in direct response to the excited-statehypothesis of Koch & Hummel (Phys. Rev. D 110, 073004, 2024). The mechanism generates a directly falsifiable prediction: τ_β (t₀) = τ_β (∞) + ΔΓ · exp (−t₀ / τ_γ) with τ_β (∞) ≈ 877–878 s, ΔΓ ≈ 10 s, and τ_γ ~ 5–30 s. This drift should be observable in beam experiments by systematically varyingthe neutron age (time elapsed since production) at the point of measurement.