Quantization of Conflict Resolution Models via Complex Wave Functions: A Wave-Mechanical Reconstruction of GMCR

[English Abstract]
This paper proposes a novel mathematical framework that maps the three fundamental parameters of the Graph Model for Conflict Resolution (GMCR)—"Preferences," "Morphisms," and "Stability"—onto a complex plane and the wave functions of quantum mechanics. In contrast to the discrete and static descriptions found in conventional category-theoretic approaches (C-GMCR), our model directly incorporates the raw dynamics of human emotions, such as "anger" and "malice," into the off-diagonal elements of the Hamiltonian (total energy matrix) as "complex phase interference effects." Through numerical simulation using a 4×4 complex matrix via Python, we mathematically demonstrate that when mutual distrust reaches its extreme (anti-phase), emotional interference completely overrides pragmatic utility, triggering a discontinuous quantum phase transition of the entire social system's ground state from "coexistence" to "mutual destruction."