  We establish that the asymptotic mean action and the asymptotic linking
number of irrational pseudo-rotations remain well-defined everywhere and
constant for every $C^{1}$ irrational pseudo-rotation that behaves as a
rotation on the boundary. As a consequence, we demonstrate that the isotopy of
irrational pseudo-rotations with a positive rotation number is a right-handed
isotopy in the sense of Ghys.
