The MESA Method: Mono-Variable Extreme Scale Analysis for Revealing Geometric Structure in Nonlinear Coupled Equation Systems

Description/Abstract: This paper formalizes a mathematical methodology — the MESA Method — for revealing the geometric structure of nonlinear coupled equation systems. The method isolates a single driving variable, holds all other parameters fixed, extends the driving variable across extreme orders of magnitude, and observes the geometric morphology of coupled variables as they respond. The output is not a solution. It is a shape. The shape reveals what the equations are.To validate the method, it was first calibrated against a known standard: Mandelbrot's equation z → z² + c, the most studied fractal in mathematics. The method correctly identified all five fractal criteria — self-similarity, power-law…