Spurious zero-dispersion continua in full $(2,q)$-positivity: A linear hierarchy-depth lower bound from an exactly solvable counting operator

Variational two-particle reduced-density-matrix methods impose hierarchies of semidefinite constraints. We ask whether a fixed level of such a hierarchy can recover even an elementary many-fermion spectrum, using the dispersion test, in which a value is accepted as an eigenvalue when the minimized