We consider the Boussinesq equation on the line for a broad class of Schwartz initialdata 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 10 main sectors describing theasymptotic behavior of the solution, and for each of these sectors we gave an exact expression for theleading asymptotic term. In this paper, we give a proof for the formula corresponding to the sectorxt\in (0,1\surd 3)