Majorana Was Right: The Neutrino's Double Identity, 89 Years Later

In April 1937, Ettore Majorana proposed that the neutrino might be identical to its antiparticle. This paper proves it is not a conjecture—it is a theorem. Any neutral spin-1/2 fermion on a four-dimensional Lorentzian spin manifold with w_2(M) = 0, admitting a CPT-stable vacuum sector and carrying no unbroken gauge U(1) charge, must be a Majorana fermion. The proof rests on the CPT theorem, Atiyah-Bott-Shapiro classification, and Bott periodicity.