A Homological Characterization of Exceptional Points in PT-Symmetric Scattering Systems: Tor₁ and Coherent Perfect Absorption

We give a homological characterization of coherent perfect absorption (CPA) in PT-symmetric two-port scattering systems. We prove a canonical isomorphism Tor^R_1(coker S, R/m) ≅ ker S(ω₀), arising from the boundary map in the long exact sequence of Tor. In particular, Tor^R_1(coker S, R/m) ≠ 0 if and only if coherent perfect absorption occurs at ω₀. This recasts exceptional points as homological singularities, providing a bridge between homological algebra and non-Hermitian physics.