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

This work establishes the collapse of particle ontology within high-energy experimental frameworks by demonstrating the absence of direct ontological access in collider-based measurements. Starting from a closed quartic variational functional, the admissible configuration space is constructed, the Hessian operator is derived explicitly, and all observable content is shown to be fully contained in its spectral structure. We prove that experimental outputs consist exclusively of structured sets of observables (tracks, timing, energy deposits), which are mapped into particle labels through a classification procedure. No element identified as a particle is ever directly measured. In particular, the Muon g-2 experiment is analyzed in detail, showing that the measured quantity is a functional of reconstructed events and belongs to the spectral content of the Hessian operator, rather than to an independent physical entity. A general theorem of non-direct ontological access is formulated and proven: for any experimental chain D → E → M(E), the assigned particle label M(E) does not belong to the set of observables and therefore cannot be identified with a physically existing object. Consequently, particles are not elements of physical ontology but emerge as classification outputs applied to structured experimental data. The introduction of additional degrees of freedom to match experimental observations is shown to be a formal signature of non-closure. In contrast, the variational framework generates all observable structures without external entities, establishing a closed, self-consistent description in which physical reality coincides with the globally selected configuration. The central result is that no particle is ever observed, and no particle is required. All experimentally accessible quantities are spectral manifestations of a single variationally selected structure.