Collapse of Particle Ontology and Non-Closure of High-Energy Experimental Frameworks

This paper demonstrates that the ontology of particles is not supported by the operational structure of high-energy experiments. Starting from a closed quartic variational functional, the admissible configuration space is constructed, the Hessian operator is derived, and all observable quantities are shown to belong to its spectral structure. We prove that experimental outputs consist of structured sets of observables (tracks, timing, energy deposits) which are mapped into particle labels through a classification procedure. No particle is directly measured at any stage of the experimental chain. The Muon g-2 experiment is analyzed as a representative case, showing that the measured quantity is a functional of reconstructed events and belongs to the spectrum of the Hessian operator. A general theorem of non-direct ontological access is established: for any experimental pipeline D → E → M(E), the assigned particle label does not belong to the set of observables and therefore cannot be identified with a physically existing object. Particles are thus reinterpreted as classification outputs associated with structured event patterns, not as elements of fundamental ontology. The results imply that frameworks requiring independent particle entities are not closed. In contrast, the variational framework provides a closed and self-consistent description in which all observables emerge from a single globally selected configuration.