  In the minimal gravitational sector of the Standard-Model Extension, there is
a coefficient whose physical consequences are unknown, and the reason behind
this lack of effects is still puzzling. This contribution summarizes several
studies where the goal was to find a fundamental explanation of this puzzle. So
far, no evidence of such a fundamental explanation has been found, suggesting
that this coefficient could actually produce physical effects. Nevertheless,
while looking for this fundamental reason, several relevant lessons have been
revealed.
