Definition: Same-target Ward-repair data

Suppose:

1. the complete insertion $J_{\mathcal{R}}{\mathcal{O}}_{\mathrm{cl}}$ and the retained Ward operation ${\mathcal{D}}_{\mathcal{R}}$ are defined on one specified domain;

2. their classical leading Ward variation is zero;

3. the complete retained quantum breaking is a defined element $B$ of a vector space $V$ of gauge-parameter-dependent operator coefficients:

   $${\mathcal{D}}_{\mathcal{R}}(J_{\mathcal{R}}{\mathcal{O}}_{\mathrm{cl}})=\hslash B(\mathrm{mod}{s}^3,{\hslash }^2);$$

4. the admissible quantum corrections form a specified vector space ${\mathcal{C}}_{\mathrm{adm}}$, including their actual observable images, and their Ward image is the linear map

   $$L:{\mathcal{C}}_{\mathrm{adm}}⟶V.$$

All coefficients are taken through $s^2$.