Ah yep, true. I'd forgotten you can still get the saddle effect from higher-order derivatives, the Hessian eigenvalues aren't enough to characterise it.
I was thinking of examples like (x-y)^2 at zero, although I guess that's still a local minimum, just not a unique local minimum in any neighbourhood.
I was thinking of examples like (x-y)^2 at zero, although I guess that's still a local minimum, just not a unique local minimum in any neighbourhood.