Digressions on the Euler Characteristic (M₃): Unlocking Pore Network Topology for Non-Equilibrium Infiltration

This post extends the discussion of [ Minkowski functionals ] by exploring the deepest topological aspects of M₃—the Euler characteristic. In our previous posts on Minkowski functionals, we established that M₀ (volume), M₁ (surface area), and M₂ (curvature) are purely geometric measures. They tell us about size, shape, and form. But M₃—the Euler characteristic—is fundamentally different. It's a topological invariant that captures something geometry alone cannot: how the pore space is connec