Planetary Magnetic Polarity Reversal as a Mass-Driven Resonance Instability in USP Field Theory

Core Proxy Definition Ξ(t) = (1 / (ρ₀ V)) ∫_V [ρ(r, t) − ρ_ref(r)] w(r) dV Threshold Condition Ξ_crit ≈ 10^(-3) Instability Criterion Ξ(t) > Ξ_crit ⇒ Dipole Instability Coherence Mapping k(t) = 1 / (1 + exp[β (Ξ(t − τ) − Ξ_crit)]) Dipole Moment M(t) = M₀ k(t) + ε(t) Mean-Field Coupling ∂B/∂t = ∇ × (α(Ξ) B) + η ∇² B α(Ξ) = α₀ (1 − Ξ / Ξ_crit) Magnetic Reynolds Number R_m = U L / η Minimal Dynamical Model dΞ/dt = S(t) − γ Ξ dκ/dt = −λ [κ − K_∞(Ξ)] K_∞(Ξ) = 1 / (1 + exp[β (Ξ − Ξ_crit)])