Definition: Remaining common-frequency obligation

For the fixed weighted graph family, the remaining obligation is:

1. establish a distributional limit through every noncoincident characteristic configuration in ${X_{\Gamma }}^{\circ }$;

2. retain the full tensor and branch summation when deciding whether singular contributions cancel;

3. show that admissible changes of auxiliary regularization give the same off-collision prescription, or differ only by the permitted collision-supported ambiguities after extension;

4. preserve the prescribed values on the strictly ordered attachment domains.