Samsonov–Shur's conjecture on the Abelian repetition threshold

For a finite alphabet of size $k$, let ${\sf ART}(k)$ be the infimum of the real numbers $\alpha$ for which there exists an infinite $k$-ary Abelian $\alpha$-power-free word. The known lower bounds are

$${\sf ART}(4)\ge \frac{9}{5},\qquad {\sf ART}(k)\ge \frac{k-2}{k-3}\quad\text{for }k\ge 5.$$

Samsonov–Shur's conjecture. The exact values are

$${\sf ART}(2)=\frac{11}{3};\qquad {\sf ART}(3)=2;\qquad {\sf ART}(4)=\frac{9}{5};\qquad {\sf ART}(k)=\frac{k-2}{k-3}\quad\text{for }k\ge 5.$$

At the time of the paper, no exact values of ${\sf ART}(k)$ were known; the conjecture was proposed by Samsonov and Shur as a tightness assertion for their lower bounds. The present paper investigates these thresholds experimentally and shows that the proposed values are not correct in several cases.