Poisson level statistics: mean = variance = 1, P(0) = 1 (exact)

Closed-form check of the Berry-Tabor conjecture's Poisson spacing distribution. Normalisation: ∫₀^∞ exp(-s) ds = 1. First moment: ⟨s⟩ = ∫₀^∞ s·exp(-s) ds = Γ(2) = 1. Second moment: ⟨s²⟩ = ∫₀^∞ s²·exp(-s) ds = Γ(3) = 2. Variance: σ² =…