Computational artifacts

kinds (symbolic/structural versus finite exact). As in Section sec:l0(d) and XVI-K, Appendix app:script, three kinds of evidence are distinguished:

• Symbolic constructions: exact polynomial identities in independent jet coordinates, valid for all smooth fields (e.g.\ the polarized source expansion and the Euler identity S1 in source_full.py).

• Coefficientwise structural checks: properties verified monomial by monomial on such a symbolic polynomial (homogeneity, slot symmetry, derivative budgets, ${\mathcal{V}}_{\mathrm{K}}\subseteq {\mathcal{V}}_{\mathrm{adm}}$, jet bounds, coherence constraints).

• Finite exact tests: exact rational evaluation on specified test data (e.g.\ agreement of ell_3 with XVI-K's ell3_of on two random $s$-dependent fields). Agreement on those cases is not a coefficientwise equivalence proof of independent implementations, and the symbolic constructions do not rest on it.

A statement is called “Proved locally” only if it has a written argument in this note; a statement supported only by the script is called “Computationally verified” and its kind of evidence is named.