Arnold–Thom conjecture for gradient flow lines

Let $f$ be a real analytic function on an open set $U\subset\mathbb{R}^n$, and let $x(t)$ be a gradient flow line of $f$ with a limit point $x_0\in U$. Arnold–Thom conjecture. If $x(t)$ has a limit point $x_0\in U$, then the limit of the unit tangents

$$\frac{x'(t)}{|x(t)|}$$

at $x_0$ exists. This conjecture concerns the asymptotic direction of gradient trajectories near limit points and is presented in the source as remaining open.