Existence of the limiting slope of three-dimensional Wythoff Nim P-positions

Let $v(n)=(v_1(n),v_2(n),v_3(n))$ denote the $n$th P-position of three-dimensional Wythoff Nim, with $n\in\mathbb N$. Define the coordinatewise normalized positions by

$$\left(\frac{v_1(n)}{n},\frac{v_2(n)}{n},\frac{v_3(n)}{n}\right).$$

Limiting-slope conjecture. The limit

$$(\alpha,\beta,\gamma):=\lim_{n\to\infty}\left(\frac{v_1(n)}{n},\frac{v_2(n)}{n},\frac{v_3(n)}{n}\right)$$

exists.

The existence of this limit would make precise the observed approximation of the P-positions by a half-line from the origin. The supplied text does not state whether the conjecture has been proved or disproved.