KK residues: χ''(ω) Lorentz poles at ω₀ ± iγ → residues ∓i/2 (causality)

Sympy-exact symbolic witness of the Kramers-Kronig contour-residue structure for a canonical Lorentzian absorption profile. Setup: ω, ω₀, γ sp-symbols positive-real. Absorptive part χ''(ω) = γ/((ω₀ − ω)² + γ²) with complex-analytic…