Definition: Admissible finite residual task

An admissible task specifies:

1. one of the local coefficient expressions generated by the finite Hamiltonian, its master residual, or a specified tested generator identity;

2. an actual density or Euler-expression representative, or a complete compact integral modulo divergences;

3. a finite exterior algebra $\Lambda ({\vartheta }_1,\dots ,{\vartheta }_d)$, with an ordered monomial basis;

4. supplied smooth field and antifield coefficients, and any compact observation tests;

5. one real coefficient extraction in that ordered basis;

6. a finite report rule and a supplied value, rational enclosure, or analytically proved status.

A released dictionary contains finitely many such tasks.