Folklore torsion-freeness conjecture for pure graph braid groups

Let $\mathsf{\Gamma}$ be a graph and let $k\geq 0$. Write $F_k(\mathsf{\Gamma})$ for its $k$-point configuration space. Folklore torsion-freeness conjecture. The space $F_k(\mathsf{\Gamma})$ has torsion-free homology for every graph $\mathsf{\Gamma}$ and every $k\geq 0$. This conjecture reflects the widespread observation that no torsion is currently known in the homology of pure graph braid groups. The paper proves only that any torsion, if present, grows slowly relative to the overall asymptotic growth, so the conjecture remains open.