Corollary: Order obstruction

Let

where the first coefficient is fixed by (eq:A1g). No choice of ${{\mathcal{A}}_{f,g}}^{(2)}$, including any finite modification beginning at order ${\kappa }^2$, makes this expression invariant under (eq:free-representative-identification) on the entire stated domain.

Proof. Formal equality requires equality of the coefficient of $\kappa$. Theorem thm:plateau-obstruction supplies a nonzero difference in that coefficient. Terms beginning at order ${\kappa }^2$ do not alter it.