(for detailed review see manuscript):

If the interactions are strictly V-A (left-handed) and if all masses

vanish, one can always find a Lagrangian "L_M(equivalent)" for which a Majorana

neutrino is phenomenologically completely equivalent to a Weyl

neutrino with a Lagrangian "L_W".

As long as there is no reason to prefer one of these Lagrangians (and

there was none in the 1950s), this means complete equivalence.

The standard model predicts L_W quantitatively - independent of

measured neutrino properties. From this the Lagrangian of

a Majorana neutrino with SM interactions "L_M(SM)"

can be determined (but the fact that it can, does not

automatically prove equivalence).

The manuscript shows that L_M(SM) is different from L_M(equivalent).

Weyl neutrinos can have Majorana masses. Therefore the manuscript's

conclusion "If the SM is quantitatively valid, neutrinos are
Weyl fermions",

does not exclude fermion-number violating processes.