Principal-plane comparison

For a non-Gaussian input the same purification proof gives

provided these moments are finite. Otherwise the trivial bound one remains valid. A proposed correction must justify its own participating-mode moments; the baseline's Wick estimate cannot be transferred to it.

Figure fig:plane is the comparison between the desired packet plane and the plane spanned by the compact tests. A small weighted residual can still be a normalized mode of large occupation. The bound uses the residual occupations, not the norm of the residual alone.