B1: the completed kernel

The relevant comparison criterion from XI-G is

Its role is comparison after a new compact kernel has been defined. It does not define that kernel.

For a corrected density-ramped model, the completed kernel must include:

1. both metric slots of the actual cubic Euler source, including its ramp-derivative terms;

2. the metric retarded leg with the XI-track normalization;

3. the coordinate leg with its own divergence-form ramp;

4. the scalar-response part of ${\mathcal{A}}_1$, including the switch and massive advanced scalar leg after transposition;

5. every support and properness condition used in the composition.

Checking only a smooth weight on the local metric diagonal would leave the scalar completion untested.

No new $u^{\sigma }$ or $W_{u^{\sigma }}$ is defined here. Accordingly no wavefront inclusion, admission criterion evaluation, or forbidden tuple for that new object is asserted.