The purpose of this article is to establish a new intrinsic characterization of the principal type schemes (or pts's for short) of the approximate normal $\lambda$-terms (or approximate normal forms). This is done by defining a correspondance between cut-free proof nets, $\beta$-normal $\lambda$-terms and their principal type schemes, and better, by defining a correspondance between approximate cut-free proof nets, approximate normal terms and their principal type schemes.