  We consider the Boussinesq equation on the line for a broad class of Schwartz
initial data for which (i) no solitons are present, (ii) the spectral functions
have generic behavior near $\pm 1$, and (iii) the solution exists globally. In
a recent work, we identified ten main sectors describing the asymptotic
behavior of the solution, and for each of these sectors we gave an exact
expression for the leading asymptotic term. In this paper, we give a proof for
the formula corresponding to the sector $\frac{x}{t}\in
(0,\frac{1}{\sqrt{3}})$.
