This work provides a structural analysis of resonance signals observed in high-energy experiments, with specific application to tetraquark and pentaquark claims reported by LHCb. Starting exclusively from a closed quartic variational functional, together with its stationary condition, Hessian spectral structure, and global decisional selection operator, we establish a rigorous distinction between physically existing configurations and experimentally generated events. Physical existence is defined uniquely by the selected stationary configuration, while all experimentally accessible configurations are shown to be non-stationary, externally sustained, and therefore non-physical in the ontological sense. Observable quantities are expressed as functionals of laboratory configurations, implying that all reconstructed structures, including invariant mass peaks, are features of event-dependent distributions. We prove that the mapping from observables to physical configurations is non-invertible, and that resonance peaks do not uniquely determine underlying structures. Consequently, tetraquark and pentaquark signals are shown to be non-stationary event structures arising from the reconstruction procedure, rather than physically existing composite objects. The results follow exclusively from the internal variational structure, without introducing particles, quark degrees of freedom, fitting procedures, or external theoretical assumptions.
Livolsi Edoardo (Mon,) studied this question.