Locality tensor-product conjecture

Let $(E,\top)$ be a locality vector space, and let $V$ and $W$ be locality vector subspaces of $E$. The locality tensor product $V\otimes_\top W$ is equipped with the quotient locality relation, denoted $\ttop$. Locality tensor-product conjecture. The pair $(V\otimes_\top W,\ttop)$ is a locality vector space. This is a central unresolved issue in the theory of locality structures; the source notes that the claim holds in many cases of interest, but no general proof is given.