Our group has described the electron reorganizations along a reactive coordinate in the ground and electronically excited states following the determinant of Hessian at all potentially degenerate CPs and their relative distance. This procedure guarantees a rigorous application of BET proposal by recovering the fundamentals underpinning Thom's works and leading to surprising findings. Furthermore, by combining this robust version of BET and other topological concepts, we have recently proposed a model for predicting the activation energy of organic and organometallic reacting systems at 0 K. In the seminal work of Silvi et al. the inversion of ammonia, the dissociation of ethane into two CH3 radicals, and the N-B bond scission of BH3NH3 molecules were used as prototypical examples to show the BET capabilities. The electronic preparation stages of ethane C-C bond scission were described through an elliptic umbilic and three simultaneous folds. The bond between the two carbons finally cracks following a cusp function. On the other hand, they rationalized the umbrella inversion via two elliptic umbilic polynomials. The topographical description of the dative bond breakage comprises one elliptic umbilic and four fold bifurcations. Despite the cryptic character of the assigning, this methodology is now a standard tool for studying different bonding situations and gaining deeper insights into chemical reactivity in a wide range of research fields. The amount of accumulated data available due to the widespread usage of BET covering several research fields has led some authors to point out that only these unfoldings (fold, cusp, and elliptic umbilic) have a precise chemical meaning. However, the elliptic umbilic contains three parameters, which must be associated with real objects controlling the reaction. Typically, the distance between two reacting centers is employed as a parameter, leaving the physical interpretation of the other coefficients unclear.