Proposition: Agreement only on the good set is insufficient

Suppose two candidate distributions agree on ${U_{\Gamma }}^{\mathrm{good}}$. Their difference is not thereby proved to be a member of ${\mathfrak{C}}_{\mathrm{part}}$.

To identify it as a permitted ambiguity, agreement on the full collision complement and the remaining contact-class conditions must also be established.

Proof. Agreement on an open set only places the support of the difference in its complement. That complement can contain noncoincident characteristic configurations as well as collisions. A distribution supported on such a characteristic locus need not be collision-supported.

Membership in ${\mathfrak{C}}_{\mathrm{part}}$ additionally restricts normal derivative order, spectator structure, external weights, normalization, and well-defined composition. Support alone does not verify those requirements.