# soft SVM - degenerate case

According to "A Note on Support Vector Machine Degeneracy", Theorem 4, if the dual problem for soft-SVM has a solution with $\alpha_i \in \{0,C\}, \forall i$, then $w=0$ for the primal problem.

In "Uniqueness of the SVM solution", there is an example which, I say, contradicts the theorem above:

Data: $x_1 = 1, y_1 = +1; x_2 = -1, y_2 = -1$

$C \in (0,1/2]$

Result: $\alpha_1 = \alpha_2 = C$

$w=2C \neq 0$.

Am I missing something?