The free traced symmetric monoidal category conjecture for the trace functional

Let $T$ be the underlying structure and let $\operatorname{TSMC}(T)$ denote the category constructed from $T$ using the trace functional as in the paper. A traced symmetric monoidal category is a symmetric monoidal category equipped with a trace operation satisfying the traced-category axioms. Free traced symmetric monoidal category conjecture. The trace functional gives $\operatorname{TSMC}(T)$ the structure of the free traced symmetric monoidal category over $T$. This would show that the construction provides the universal traced symmetric monoidal category generated by $T$, and would also support the subsequent construction of compact closed categories. The supplied text gives no evidence that the conjecture has been resolved.