  Recently, we proposed a novel entry of the pp-wave holographic dictionary,
which equated the Berenstein-Maldacena-Nastase (BMN) two-point functions in
free $\mathcal{N}=4$ super-Yang-Mills theory with the norm squares of the
quantum unitary transition amplitudes between the corresponding tensionless
strings in the infinite curvature limit, for the cases with no more than three
string modes in different transverse directions. A seemingly highly non-trivial
conjectural consequence, particularly in the case of three string modes, is the
non-negativity of the BMN two-point functions at any higher genus for any mode
numbers. In this paper, we further perform the detailed calculations of the BMN
two-point functions with three string modes at genus two, and explicitly verify
that they are always non-negative through mostly extensive numerical tests.
