  The Alternative Hypothesis concerns a hypothetical and unlikely picture of
how zeros of the Riemann zeta function are spaced which one would like to rule
out. In the Alternative Hypothesis, the renormalized distance between
nontrivial zeros is supposed to always lie at a half integer. It is known that
the Alternative Hypothesis is compatible with what is known about the pair
correlation function of zeta zeros. We ask whether what is currently known
about higher correlation functions of the zeros is sufficient to rule out the
Alternative Hypothesis and show by construction of an explicit counterexample
point process that it is not. A similar result was recently independently
obtained by T. Tao, using slightly different methods.
  We also apply the ergodic theorem to this point process to show there exists
a deterministic collection of points lying in $\tfrac{1}{2}\mathbb{Z}$ which
satisfy the Alternative Hypothesis spacing but mimic all statistics which are
currently known about zeros of the zeta function.
