The Lucian Method — Control Group Validation: Applying Mono-Variable Extreme Scale Analysis to Mandelbrot's Equation z → z² + c

Description: This paper establishes the foundational control group for the Lucian Method (Mono-Variable Extreme Scale Analysis). The method is applied without modification to Mandelbrot's equation z → z² + c — a system whose fractal geometry is already proven. All five fractal classification criteria are confirmed: self-similarity, power-law scaling, fractal dimensionality, bifurcation cascade with Feigenbaum universality, and fractal Lyapunov structure — across 12 orders of magnitude. The instrument is calibrated against a known standard, validating its prior application to Einstein's field equations and the Yang-Mills equations.