On the general structure of nonlinear equations integrable by the general linear spectral problem

Two beams of indistinguishable fermions from independent sources cannot produce an interference pattern that changes when the wavefunction of each single-fermion state for one beam is multiplied by — 1; they cannot produce interference the way photons from independent sources can. This means the changes in neutron interference caused by a magnetic field applied to one of the beams cannot be interpreted as equivalent to changes that could be made by rotating the source of one beam by 2π radians. If it is assumed that rotation by 2π radians cannot be observed, the argument made here becomes a simple proof that particles with half-integral spin cannot be bosons.