Occupation and flux are not dimensions

Quasifreeness and covariance data can identify geometric or multimode Gaussian packet states under the additional assumptions in Cheung's En02-E and Em03-B records CheungEn02E,CheungEm03B. Those assumptions are stronger than a selected mean.

For a known geometric state, truncation through level $K$ has tail $z^{K+1}$. The normalized truncated marginal has trace distance $z^{K+1}$ from the original marginal. The normalized truncation of its standard pure purification instead has trace distance $\sqrt{z^{K+1}}$. These follow from the orthogonal tail and pure-state overlap. They are state-specific estimates, not a uniform whole-code diamond certificate.