The Cartan-Kuranishi theorem guarantees that a PDE or EDS can always be completed, by prolongation, to involution. My question is, and this is quite murky to gauge from the literature, whether Cartan's equivalence method (where prolongation and normalization of essential torsion is a little bit different from the standard prolongation of PDE and EDS) terminates at involution as an easy consequence of Cartan-Kuranishi.

Some authors claim that this is so while others say that termination of Cartan's method has never really been proven, notably Bryant, Griffiths and Hsu in the introduction to this paper: https://publications.ias.edu/node/262