Proposition: Rigidity of collision-supported changes

Every defined contact change in ${\mathfrak{C}}_{\mathrm{part}}$ for this graph restricts to zero on $V$. Consequently any two graph constructions whose difference belongs to the frozen ${\mathfrak{C}}_{\mathrm{part}}$ have the same restriction to $V$.

Proof. Each term (eq:Cpart) has support in its specified collision locus. Differentiation does not enlarge support; nor does multiplication in a defined product. The finite sum is supported in the collision union. Its restriction to the disjoint neighborhood $V$ is zero.