  Using an analytical result for the eigensystem of the linearized collision
term for a classical system of massless scalar particles with quartic
self-interactions, we show that the shear-stress linear response function
possesses a branch-cut singularity that covers the whole positive imaginary
semi-axis. This is demonstrated in two ways: (1) by truncating the exact,
infinite linear system of linear equations for the rank-two tensor modes, which
reveals the cut touching the origin; and (2) by employing the Trotterization
techniques to invert the linear response problem. The former shows that the
first pole tends towards the origin and the average separation between
consecutive poles tends towards zero as power laws in the dimension of the
basis. The latter allows one to obtain the response function in closed form in
terms of Tricomi hypergeometrical functions, which possess a branch-cut on the
above-mentioned semi-axis. This suggests that the presence of a cut along the
imaginary frequency axis of the shear stress correlator, inferred from previous
numerical analyses of weakly coupled scalar $\lambda \varphi^4$ theories, does
not arise due to quantum statistics but instead emerges from the fundamental
properties of this system's interactions.
