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…