The first changes in the locality of each carbon take place as the relative separation between s1a and the three saddles of index two (s2a, s2b, and s2c) decreases. Since the Poincaré-Hopf formula 54 dictates both the number and type of CPs variations, only one of the three saddles of index two is involved in the bifurcation, as presented in Figure , Panels a and b. We again relied on the |det H| at CPs and their relative distance to determine that such a saddle is s2a, meaning that this point and s1a coalesce, and thus, the latter CP does not change its index but rather disappears through a bifurcation that cannot be rationalized using any unfolding; As the CC bond further stretches, an index-two saddle (s2d) and one repellor (m4) arise in the vicinity of the remaining points, s2b and s2c.