GOE (β=1): P(s) = πs/2·e^{-πs²/4}
GUE (β=2): P(s) = 32s²/π²·e^{-4s²/π}
Poisson: P(s) = e^{-s}

Level repulsion: P(s) ~ sᵝ near s=0
GOE: β=1, GUE: β=2, GSE: β=4

Wigner surmise: exact for 2×2,
excellent approximation for N→∞

Integrable systems → Poisson
Chaotic systems → Wigner-Dyson