An explicit presentation model

For one normal coordinate,

Under the printed inverse-Fourier convention, ${\mathcal{F}}^{-1}(\mathrm{i}\theta )={\delta }^{\prime }$, hence

while its two summands reconstruct separately to $-\delta (q)R_{\mathrm{ret}}(r)$ and $\delta (q)R_{\mathrm{ret}}(r)$. This proves why a highest presentation degree alone is not an intrinsic joint symbol. One may define an image filtration, but its associated symbols must respect every reconstruction identity.