Universal area-decay exponents in K-parameterized non-holomorphic iterations

We study the family of non-holomorphic complex iterations zn+1 = Kzng(Im(zn))+c, parameterized by K > 0 and a real-valued function g. We prove an exact Decoupling Lemma, derive a closed-form two-step stability boundary, and establish that the stable parameter-space area satisfies A(K)∼C(α,g0,R) K−γ with universal exponent determined by the vanishing order α of g at the operating point. This yields three universality classes: Class A (g(0) >0, γ = 2), Class B (odd zero, γ = 1 with logarithmic correction), and Class C (infinite-order zero, anomalous logarithmic scaling). We verify the predicted exponent to 0.2% precision across eight functions spanning six independent scientific fields, including non-integer exponents (α= 1/2, γ = 4/3, verified to 0.14%; α = 3/4, γ = 8/7, verified to 0.08%) and a super-linear exponent (α = 2, γ = 1/2, verified to 0.01%), and demonstrate a continuous Class B→A interpolation via ˜ g(y) = tanh(y+ a). The formula γ = 2/(1 + α) is proved for 0 1 is proved with γ = 1/α and exact constant involving sin(π/α) (Theorem 5, Case 2). The two cases cover all α>0 and join continuously at α= 1. Of three original open problems, all are resolved: OP-4 (exact Lambert W crossover formula, Equation (11), and full n-step envelope characterised, Proposition 9), OP-5 (Proposition 10, super-exponential subdominance, rigorous for all Class AB-regular g), and OP-1 (CB(R) = 2R exactly, Corollary 6). This classification has no known analogue in the Mandelbrot, Multibrot, or Burning Ship fractal literature.