The frozen partial-diagonal class

For the source comparison, the supplied XIII-C class is reproduced: before pushforward a permitted contact change has form

Here:

1. $r_I$ is transverse to a specified collision diagonal ${\Delta }_I$;

2. $S_{\Gamma /I}$ is the inherited spectator coefficient, with its two remaining field slots retained;

3. $w_{\Gamma }$ is built from the already present smooth graph weights and $g,\partial g,{\sigma }_{\epsilon },{\sigma }_{\epsilon }^{\prime },{\sigma }_{\epsilon }^{\prime \prime }$;

4. $D_{\Gamma }$ is the fixed finite graph differential operator;

5. the change is even, has ghost number zero and field degree two, and lies in the existing compact graph closure;

6. it preserves the tree datum and observable-subgraph normalizations;

7. the product and pushforward in question must already be well defined.

Finite sums give ${\mathfrak{C}}_{\mathrm{part}}$; total-diagonal terms give ${\mathfrak{C}}_{\mathrm{tot}}\subseteq {\mathfrak{C}}_{\mathrm{part}}$. The bound six is frozen bookkeeping, not a new power-counting theorem CheungXIIIC,CheungXIIIE. The exact graph catalogue is still required for an inherited application.