Asymptotic existence of symEF1 allocations

Consider instances with a fixed number $n$ of agents and $m$ items, with probability taken over the paper's instance model. A symEF1 allocation is an allocation satisfying symmetric envy-freeness up to one item. Asymptotic existence conjecture. For any fixed number of agents $n$, as the number of items $m$ tends to infinity, the probability that an instance has a symEF1 allocation tends to $1$. The conjecture is motivated by simulations showing that the proportion of symEF1 instances increases rapidly with the number of items; it remains open.