Graph-Weighted Projections of Quantum Channels as Structural Diagnostics for Open-System Model Discrimination

This preprint introduces Φ_struct, a graph-weighted structural functional defined on quantum channel and interaction-graph pairs. The framework is motivated by the established non-uniqueness of open quantum-system realizations, where distinct microscopic interaction architectures can generate identical Lindblad dynamics while differing at the process level. The proposed functional combines the Choi representation of a quantum channel with a graph-derived locality tensor to provide a computationally inexpensive structural diagnostic for comparing candidate interaction architectures. Formal properties are established, including invariance on fixed graph-assigned Lindblad equivalence classes and discrimination between graph-distinct implementations sharing identical reduced dynamics. An illustrative two-environment model demonstrates nonzero structural separation under equalized decoherence rates. The work does not modify quantum mechanics and does not attempt to replace process-tensor methods. Instead, it provides a graph-based organizational framework for studying interaction topology in open quantum systems.