Fraenkel's conjecture on complementary Beatty sequences

Let $d\geq 3$, let $\alpha_1<\alpha_2<\ldots<\alpha_d$, and let $\gamma_1,\ldots,\gamma_d$ be real numbers. Suppose that the vectors

$$(\lfloor n\alpha_i+\gamma_i\rfloor)_{i=1}^d,$$

for $n\in\mathbb{N}$, split the positive integers. Fraenkel's conjecture. Then

$$\alpha_i=\frac{2^d-1}{2^{d-i}},\qquad i=1,\ldots,d.$$

This is the nonhomogeneous rational-modulus form of Fraenkel's conjecture on partitions of the positive integers by Beatty-type sequences. The statement concerns the uniqueness of the moduli, while the shifts $\gamma_i$ are unrestricted; the source presents it as a conjecture and gives historical references to work on special cases.