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The aim of this paper is to apply ideas from the study of Legendriansingularities to a specific example of interest within mirror symmetry. Wecalculate the Landau-Ginzburg $A$-model with $M= \mathbb C^3, W=z_1 z_2 z_3$ inits guise as microlocal sheaves along the natural singular Lagrangian thimble$L = {\mathit Cone}(T^2)\subset M$. The description we obtain is immediatelyequivalent to the $B$-model of the pair-of-pants $\mathbb P^1 \setminus \{0, 1,\infty\}$ as predicted by mirror symmetry.

A combinatorial calculation of the Landau-Ginzburg model $M= \mathbb C^3, W=z_1 z_2 z_3$