Algorithm 5 Kropotov–Pakhomov recurrent network with spectral-normalized recurrent matrix.

Input: 1D map P(x), neural size candidates M = {m1, …, mr} Output: optimal neural dimension m* 1. For each m in M: 2.   Construct MRNN(m) with spectral radius ρ(W) = 1 3.   Simulate MRNN(m) for fixed (η,γ) 4.   Extract peaks of x1: {p_k} 5.   Compare invariant set of MRNN(m) with orbit of P using:      (a) Lyapunov matching |λ_MRNN - λ_P| < ε      (b) Peak-bifurcation matching: Hausdorff distance < δ      (c) Stability window width > threshold 6. Select m* yielding minimal dimension satisfying all criteria Result: m* = 64 in all tested configurations.