In our paper The numerical measure of a complex matrix (Comm. Pure and Appl. Math. ,65 (2012), pp 287--336), T. Gallay and I proved that the restriction to some zones of the numerical density of an $n\times n$ matrix is polynomial of degree at most $n-3$. The only reason why we were led to this result is because of numerical experiments shown some evidence. Does it qualify ?
In our paper The numerical measure of a complex matrix (Comm. Pure and Appl. Math. ,65 (2012), pp 287--336), T. Gallay and I proved that the restriction to some zones of the numerical density of an $n\times n$ matrix is polynomial of degree at most $n-3$. The only reason why we were led to this result is because of numerical experiments shown some evidence. Does it qualify ?