Complexity of Reachability in Fixed-Dimensional Continuous VASS

A $d$-dimesional continuous VASS is a counter system, which consists of a finite set of states and $d$ counters, each of which can hold a non-negative rational number. A transition of such a machine consists of an integer vector $\mathbf{v} \in \mathbb{Z}^d$, which allows us to update the counters as follows: Upon taking this transition, we first select some non-zero fraction $\alpha \in (0,1]$ and then add the vector $\alpha \cdot \mathbf{v}$ co-ordinate-wise to our current counter values. Since each counter can only hold a non-negative rational number, while adding the vector $\alpha \cdot \mathbf{v}$, we have to ensure that no counter value becomes negative.

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The reachability problem for continuous VASS is the problem of deciding whether a given source configuration of a continuous VASS can reach a given target configuration. It is known that this problem is NP-complete. When the dimension $d$ is fixed and all vectors are encoded in binary, it is known that the problem is NL-complete if $d = 1$ and NP-complete if $d \ge 2$. However when $d$ is fixed and all vectors are encoded in unary, the complexity is unknown, which leads to the following question: What is the complexity of reachability in continuous VASS when the dimension $d$ is fixed?