Start the 'min' expressions

main.tex

@@ -819,6 +819,24 @@ radius of the pseudo-wall being positive
 	\frac{1}{2n^2}\ZZ
 \end{equation}
 
+For each $r$, the smallest element of $\frac{1}{\lcm(m,2n^2)}\ZZ$ strictly larger
+than the lower bound here is exactly $\frac{1}{\lcm(m,2n^2)}$ greater.
+Therefore, if any of the two upper bounds come to within
+$\frac{1}{\lcm(m,2n^2)}$ of this lower bound, then there are no solutions for $d$.
+
+Considering equations
+\ref{eqn:bgmlv2_d_bound_betamin},
+\ref{eqn:bgmlv3_d_bound_betamin},
+\ref{eqn:positive_rad_d_bound_betamin},
+this happens when:
+
+\begin{equation}
+	\min\left(
+		\sage{bgmlv2_d_upperbound_exp_term},
+		\sage{bgmlv3_d_upperbound_exp_term_alt.subs(chbv==0)},
+	\right)
+	< \frac{1}{\lcm(m,2n^2)}
+\end{equation}
 
 \minorheading{Irrational $\beta$}