arXiv2026
The occurrence of a field in a quantum field theory does not by itself establish the existence of a corresponding asymptotic particle. We formulate a structural criterion separating operator admissibility, dynamical spectral realization, and particlehood, using the exterior-polynomial classification of gravitino mass bilinears as a prototype. Particlehood is organized as an ordered filtration of geometry and state, effective algebra, dynamics, and spectral analysis, with the localization criterion $Λ[Ψ]$ defined by the presence of a physical spectral atom of non-zero weight. We obtain four results. First, conventional linearly realized global supercharges are obstructed on a positive-definite de Sitter Hilbert space when the full diagonal odd--odd bracket satisfies a positivity-reversal condition; the spacetime part is shown to be reversible in $\mathfrak{so}(4,1)$, while internal generators require a separate check. Second, invariant scalar de Sitter product decompositions remove the Minkowski additive two-particle threshold in principal-series channels. Third, a spectral-transfer decomposition shows how continuum weight in a mediator propagator can open absorptive support for an external field below the atomic mediator threshold. Fourth, in a reduced effective-operator basis, the fermionic vector derivative coupling is redundant under current-conservation assumptions, whereas the axial dimension-five coupling is physical unless excluded by parity or CP; under that symmetry hypothesis the residual fermionic derivative potential starts one operator dimension above the scalar one. Exact unbroken supersymmetry enforces multiplet rigidity of the atomic criterion.