The frozen contact class

The source additionally warns that a spectator can remain singular in its tangential variables. Smoothness concerns the external weights, not the entire spectator distribution. It also warns that differentiating a diagonal distribution can differentiate its multiplying weights upon pushforward. This is not permission to add independent arbitrary higher-jet coefficient functions.

These qualifications are retained. In particular, a polynomial weight convention introduced below is not inferred from the words “built from.” Those words do not specify a polynomial degree, a coefficient field beyond the ordinary constants, or a complete list of admissible graphwise combinations.