In a series of recent papers implementing ab initio DFT modeling with VASP, we have explored the kaolin system at zero pressure, kaolinite under pressure up to 60 GPa and the known kaolin phases under moderate pressure at 10 GPa. We summarize here the concepts, conclusions and falsifiable predictions printed in this series of papers, stressing independent and recent experimental results. A new rationalization of the kaolin system results, clarifying its stability diagram, its diagenesis and its solid-state phase transformations. The existence at moderate pressure of two new translations −a/3 and (a + b)/3, not possible at zero or low pressure, leading to five-fold coordination for Si was correctly predicted. Two newly and independently observed kaolinite polytypes (kaolinite II and III) were also correctly predicted. The existence of a still unobserved (SU) kaolinite IV phase is predicted at a pressure not higher than 60 GPa. Finally, transformations of dickite II into SU dickite III and nacrite into SU nacrite II are predicted to occur around 10 GPa. Optimized crystal structures predicted by ab initio modeling for the most likely low enthalpy polytypes are printed, which should simplify their identification when they will be observed, as they did for kaolinite II and III. Concepts developed here for kaolin minerals are generally applicable to hydrogen-bonded phyllosilicate polytypes or other hydrogen-bonded layered systems. This series of papers then implements a new way of expanding knowledge about experimentally difficult systems: inexpensive and relatively fast quantum computations can bring support to experimental results when conflicting reports exist in the literature, as well as produce predictions that are easily falsifiable experimentally, thus pointing to fruitful directions for new experiments. This loop of quantum computation followed by critical experiments results in faster and cheaper scientific progress as seen here on the kaolin system.