Green functions constitute the fundamental observables of quantum field theory and generate perturbative expansions in terms of Feynman diagrams. While individual Feynman diagrams have been extensively studied, comparatively little attention has been devoted to the classification of entire diagrammatic architecture classes. In this work, we propose a topological framework in which Green functions generate families of Feynman architectures that may be reduced to graph–holonomy structures. Propagators are interpreted as transport roads, interaction vertices as transport junctions, and Wilson holonomies as global transport cycles. We introduce a graph–holonomy invariant map assigning to each architecture class a tuple (a,b,c,d), which serves as a compact signature of its topological organization. The resulting framework is formulated as a classification theory rather than a modification of quantum field theory. Primitive architecture motifs, architecture equivalence classes, graph–holonomy invariants, architecture energy, and a principle of minimal construction are introduced. The proposed framework provides a systematic program for the topological classification of Green-function architectures generated by quantum field theories and, in particular, by Quantum Chromodynamics.
Publication Date: 2026-06-19