Capillary threshold of a reduced solidification dispersion ($R_c>27/2$)

The reduced dimensionless growth rate $g(q)=-1+q-2q^3/R_c$ has a positive maximum precisely when $R_c>27/2$. Its maximizing $q=\sqrt{R_c/6}$ follows by differentiation. At equality $q=3/2$, outside a strict $q\gg 1$ short-wave regime. The inequality is an exact criterion for the reduced cubic, not a quantitative onset theorem for full thermal stability of a travelling solidification front.