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The constants will drop out when taking the fold of this potential \begin{equation}  f_*(x)=\frac{A}{ \frac{x_2^3-x^3}{x^3-x_1^3}+ {x^3-x_1^3}{x_2^3-x^3} \frac{x^3-x_1^3}{x_2^3-x^3}  } \end{equation} which is \begin{equation}  f_*(x)=\frac{A(x^3-x_1^3)(x_2^3-x^3)}{ (x_2^3-x^3)^2 + (x^3-x_1^3)^2 }  \end{equation}  becoming reminiscant of the form \begin{equation}  k^4/k^2 +k^2  \end{equation}