Closed-form Gaussian-integral check of the Wigner GOE surmise P(s) = (π/2)·s·exp(-π·s²/4). Normalisation ∫₀^∞ P ds = 1 and unit mean ⟨s⟩ = 1 are fixed by the unfolding convention (mean level spacing set to 1). Second moment: substitute u…
Closed-form Gaussian-integral check of the Wigner GOE surmise P(s) = (π/2)·s·exp(-π·s²/4). Normalisation ∫₀^∞ P ds = 1 and unit mean ⟨s⟩ = 1 are fixed by the unfolding convention (mean level spacing set to 1). Second moment: substitute u…