Remark: Boundary freedom is not sharp under the original global hypothesis

The distinction between ${\mathrm{DF}}_{<N}$ and ${\mathrm{DF}}_{\le N}$ matters. The weaker condition supports Corollary cor:K's boundary alternative. Under the stronger, globally diagonal-faithful condition, Theorem thm:boundary removes that alternative for outcome laws. No exceptional GHZ support classification is needed.