Definition: Admissible replacement

An admissible $H^{\prime }$ is a complex-valued block bidistribution with:

1. the same shell equations in both slots;

2. the same graded antisymmetric part $i\Delta$;

3. smooth difference $d=H^{\prime }-H$;

4. ${H^{\prime }}_{AB}=0$ unless $|A|+|B|=0(\mathrm{mod}2)$ and $\mathrm{gh}(A)+\mathrm{gh}(B)=0$.