Bounds for covariance and correlation of incident arcs in uniformly random DAGs

Let $G=(V,A)$ be a directed acyclic graph, and consider two arcs incident on a common node. Incident-arc range conjecture. The covariance between the two arcs takes values in the interval $[0.08,0.140625]$ in modulus, while the correlation takes values in $[0.125,0.28125]$ in modulus. These ranges summarize values observed in complete enumerations for DAGs with three through seven nodes; their validity beyond the enumerated cases is not formally established.