The Cartan equivalence problem for Levi-non-degenerate real hypersurfaces $M^3\subset\mathbb C^2$

We develop the Cartan equivalence problem for Levi-non-degenerate $\mathcal C^6$-smooth real hypersurfaces $M^3$ in $\mathbb C^2$ in great detail, performing all computations effectively in terms of local graphing functions. In particular, we present explicitly the unique (complex) essential invariant $\mathfrak{J}$ of the problem. Comparison with our previous joint results [1] shows that the Cartan–Tanaka geometry of these real hypersurfaces perfectly matches their biholomorphic equivalence.