Crucial Dependence of ``Precarious'' and ``Autonomous'' phi^4s Upon the Normal-ordering Mass

Using the Gaussian wave-functional approach with the normal-ordering renormalization prescription, we show that for the (3+1)-dimensional massive lambda phi^4 theory, precarious'' and autonomous’’ phi^4s can exist if and only if the normal-ordering mass is equal to the classical masses at the symmetrc and asymmetric vacua, respectively.