Proof of the Fukui conjecture via resolution of singularities and related methods. IV

The present article is a direct continuation of the previous part III of this series of articles, which have been devoted to cultivating a new interdisciplinary region between chemistry and mathematics. In the present part IV, we develop two sets of fundamental theoretical tools, using methods from the field of resolution of singularities and analytic curves. These two sets of tools are essential in structurally elucidating the assertion of the Fukui conjecture (concerning the additivity problems) and the crux of the functional asymptotic linearity theorem (functional ALT) that proves the conjecture in a broad context. This conjecture is a vital guideline for a future development of the repeat theory (RST)-the central unifying theory in the First and the Second Generation Fukui Project.