Definition: Fixed contraction package

A package is

with the following fixed data.

1. $K_{\mathrm{ret}}$ is an actual complete internal distribution, with tensor slots and component duality specified.

2. The grouped crossed array is

   $${C_I}^{\mu \nu }={H_{T,\gamma }}^{\mu \nu }{}_I\otimes H_{T,\varphi }-{H_{\gamma }}^{\mu \nu }{}_I\otimes H_{\varphi }.$$

   Its four input distributions, relative arguments, prescriptions, and tensor conventions are specified. No undeclared mixed products are introduced.

3. The vertex is (eq:vertex), including fixed $m,g$.

4. $\rho \in {C_c}^{\infty }({\mathbb{R}}^8)$ is real and has integral one. Nonnegativity is not required. The cutoff $\chi \in {C_c}^{\infty }({\mathbb{R}}^8)$ equals one near $\mathfrak{f}(\overline{U})$.

5. When a reference is available, $V_{\mathrm{ref}}\subset U$ is open and $t^{\circ }\in {\mathcal{D}}^{\prime }(V_{\mathrm{ref}};E_{\mathrm{out}})$ is specified. Any claimed agreement with it requires a proof, not merely its designation as a reference.

6. ${\mathcal{C}}_{\mathrm{allowed}}$ specifies permitted scale-dependent subtractions, finite additions, and normalization rules. These are not inferred from the existence of a finite part.

7. A requested output operation includes its spaces, support conditions, maps, residual bundle, and required closed wavefront cone ${\Gamma }_{\mathrm{out}}$.

Every entry is independent of $\delta$.