Coordinate kernel and source incidence

Define the coordinate-response kernel by

For a chosen finite-order coordinate operator its kernel is a finite sum of smooth coefficients and derivatives of $R_{\mathrm{ret}}(b-a)$. This definition fixes its type. Its exact inherited signs and coefficients must be taken from the complete source, not guessed.

Let the polarized local quadratic source have kernel

It is defined by

The polarization convention is the mixed second derivative. Its coefficient list and derivative bound are part of the selected source data.

The map $(v,a,z)\mapsto (v-a,v-z)$ is a submersion. Consequently the two-delta product is defined, with support $v=a=z$ and underlying conormal covectors

The supplied XIV-H source incidence has total normal polynomial order at most two; in its stated conormal convention this gives upper order three in twelve dimensions CheungXIVH. That numerical order is not asserted for every possible cubic density in Section sec:Euler.