= Square-zone cutoff of a saddle contour
{title2=$|k_y|\leq\sqrt{\Lambda^2-\delta/A}$}
For positive detuning inside a strict square region $|k_x|,|k_y|\leq\Lambda$, substituting $k_x^2=k_y^2+\delta/A$ bounds $k_y$ by the displayed value, provided $0<\delta/A<\Lambda^2$. Integrating to $\Lambda$ instead extends the contour slightly outside that square. Either prescription has the same leading logarithmic singularity near zero detuning; it does not give the same exact finite-detuning result.
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