Using the foundational BET framework, Silvi and collaborators attempted to describe the inversion of ammonia through two elliptic umbilic functions. However, this model does not hold up when we examine the Hessian determinant at potentially involved critical points (CPs) and their relative distance. Figure illustrates the changes in the topographic map before and after the inversion. Nonetheless, it should be stressed that identifying the colliding CPs cannot be performed by a visual inspection but rather by using the mathematical principles supporting CT, which are crucial in selecting the right unfolding featuring the chemical process. Indeed, considering the Poincaré-Hopf theorem, one can assert that only two CPs coalesce, having such points different indices. Yet, no unfolding can accurately capture this topographic event, as the involved CPs are saddle points. (a) (b) (c) . Following this merger, there is an appearance of a2 and s1d near the remaining saddles, which showcases a fold catastrophe (Panel c). In the visualization, the different map features are distinguished by color: attractors are shown in purple, saddles of index one in orange, saddles of index two in yellow, and repellors in green. For ease of interpretation, gradient lines are not displayed. In addition, Lewis-like structures are provided to help understand the molecular configurations associated with these changes.