Corollary: The proposed global C2 argument is insufficient

The $Z_3$ bounds, the vertex diagonal bound, and removal of the collision loci do not prove the joint time-ordered contraction on the entire remaining configuration space.

Proof. Lemma lem:pinch supplies a nonzero cancellation at distinct vertices. At each entry the two contracted covectors may be opposite while the unused covector is zero. Their sum remains zero, so the $Z_3$ bound does not exclude them.