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At the end of the 1950s various authors proved the following theorem
(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.