In classical hard-sphere systems, the recoupling operator resolves the combinatorial explosion caused by recollisions by cutting the complex history graphs ofrecollisions and reconnecting them at coarse-grained scales, thereby completing thelong-time limit derivation from Newtonian dynamics to the Boltzmann equation.This paper generalizes this self-consistent logic to quantum many-body systems,establishing a formal framework in which Feynman diagrams are cast as constraintnetworks. Within this framework, quantum rescattering—including higher-orderloop diagrams, Efimov trimers, and BCS pairing fluctuations—is identified as anon-perturbative dominant substructure in the constraint network: these structures form high-multiplicity edges and closed loops in Feynman diagrams, leadingto a sharp rise in local connectivity. We prove that in the dilute-gas and weakcoupling scaling limits, the contribution of Feynman diagrams containing extensiverescattering to macroscopic observables is parametrically suppressed. The recoupling operator compresses higher-order loop diagrams into lower-order effectivevertices and reconnects them at larger scales, realizing a cross-scale skeleton expansion. The core result proposes a scaling limit path for the quantum Hilbertsixth problem: the limit from the microscopic quantum Boltzmann equation tothe macroscopic quantum fluid dynamics equation can be rigorously realized viathe Feynman diagram skeleton expansion and the cross-scale coarse-graining of therecoupling operator. This framework provides the missing rigorous foundation forquantum many-body effective theories