Remark

The fifth pass confirms that XIII-C's “built from” $g,\partial g,{\sigma }_{\epsilon },{\sigma }_{\epsilon }^{\prime },{\sigma }_{\epsilon }^{\prime \prime }$ does not say whether the weight space is polynomial or arbitrary smooth. The record's caution that “a bound on normal derivative order does not by itself make the ambiguity finite-dimensional” record is thus a theorem in the jet module (Corollary cor:finite) and an open reading question for ${\mathcal{C}}_{\mathrm{part}}$.