  We construct a family of small analytic discs attached to Levi non-degenerate
hypersurfaces in $\mathbb{C}^{n+1}$, which is globally biholomorphically
invariant. We then apply this technique to study unique determination problems
along Levi non-degenerate hypersurfaces that are merely of class
$\mathcal{C}^4$. This method gives 2-jet determination results for germs of
biholomorphisms, CR diffeomorphisms, as well as in the almost complex setting.
