Level-Spacing Chaos Diagnostic & Space-Time Relaxation Map

The 3D eigenstate-thermalization simulator exactly diagonalizes a small (N = 8) mixed-field Ising spin chain and shows the Eigenstate Thermalization Hypothesis at work as a chain of spheres relaxing after a quench, alongside a 3D scatter cloud of eigenstate expectation values against energy. This 2D companion keeps the identical exact-diagonalization physics but exposes it through two genuinely 2D-native views instead: a nearest-neighbor level-spacing-ratio histogram — the standard spectral chaos diagnostic that needs no reference observable, comparing the computed spectrum directly against the Poisson (integrable) and Wigner-Dyson GOE (chaotic) distributions — and a space-time heatmap that plots every site's magnetization against time as the domain-wall or Néel quench relaxes. Sliding h_z from 0 to about 0.5 turns the level-spacing histogram from a Poisson-like pile-up near zero spacing into a GOE-like repulsion hump, while the space-time map turns from persistent, oscillating stripes into a rapid wash to flat gray equilibrium.