A limit route for the complete grouped expression

The theorem assumes convergence of the full graph, not just its internal pole. For two regulators to define the same off-collision prescription, they must agree on the whole off-collision domain, not merely on the smaller canonical subset. After that agreement, membership of their difference in the exact permitted contact class is another obligation.

A direct generalized composition is an alternative route: construct

with the actual source domains, canonical agreement, descent, characteristic value, and complete wavefront. No existence theorem for that inherited composition is asserted.