  Filaments of the cosmic web drive spin acquisition of disc galaxies. The
point process of filament-type saddle represent best this environment and can
be used to revisit the Tidal Torque Theory in the context of an anisotropic
peak (saddle) background split. The constrained misalignment between the tidal
tensor and the Hessian of the density field generated in the vicinity of
filament saddle points simply explains the corresponding transverse and
longitudinal point-reflection symmetric geometry of spin distribution. It
predicts in particular an azimuthal orientation of the spins of more massive
galaxies and spin alignment with the filament for less massive galaxies. Its
scale dependence also allows us to relate the transition mass corresponding to
the alignment of dark matter halos spin relative to the direction of their
neighboring filament to this geometry, and to predict accordingly it s scaling
with the mass of non linearity, as was measured in simulations.
