Pointwise Euclidean invariants need not depend only on current curvature and torsion

For sufficiently smooth curves, $Q(\gamma ,s)={\kappa }^{\prime }(s)$ obeys Euclidean and parameter-translation covariance but is not determined by the pair $(\kappa (s),\tau (s))$. Under the bare covariance definition, nonlocal examples such as $Q(\gamma ,s)=\kappa (s+1)$ work as well.