  The Earth magnetopause, when sufficiently plane and stationary at a local
scale, can be considered as a "quasi-tangential" discontinuity, since the
normal component of the magnetic field Bn is typically very small but not zero.
Contrary to observations, the "Classic Theory of Discontinuities" (CTD)
predicts that rotational and compressional jumps should be mutually exclusive
in the general case Bn n.e.t. 0, but allows only one exception: the tangential
discontinuity provided that Bn is strictly zero. Here we show that Finite
Larmor Radius (FLR) effects play an important role in the quasi-tangential
case, whenever the ion Larmor radius is not fully negligible with respect to
the magnetopause thickness. By including FLR effects, the results suggest that
a rotational discontinuity undergoes a change comparable to the change of a
Shear Alfven into a Kinetic Alfven wave when considering linear modes. For this
new kind of discontinuity, the co-existence of rotational and compressional
variations at the magnetopause does no more imply that this boundary is a
strict tangential discontinuity, even in 1D-like regions far from X-lines if
any. This result may lead to important consequences concerning the oldest and
most basic questions of magnetospheric physics: how can the magnetopause be
open, where and when? The role of FLR being established theoretically, the
paper then shows that it can be proved experimentally. We make use of MMS data
and process them with the most recent available 4 spacecraft tools. First, we
present the different processing techniques that we use to estimate spatial
derivatives, such as grad(B) and div(P), and the magnetopause normal direction.
We point out why this normal direction must be determined with extremely high
accuracy to make the conclusions unambiguous. The results obtained by these
techniques are presented in a detailed case study and on a statistical basis.
