  Recent experiments on cold atoms in optical lattices allow for a quantitative
comparison of the measurements to the conductivity calculations in the square
lattice Hubbard model. However, the available calculations do not give
consistent results and the question of the exact solution for the conductivity
in the Hubbard model remained open. In this letter we employ several
complementary state-of-the-art numerical methods to disentangle various
contributions to conductivity, and identify the best available result to be
compared to experiment. We find that at relevant (high) temperatures, the
self-energy is practically local, yet the vertex corrections remain rather
important, contrary to expectations. The finite-size effects are small even at
the lattice size $4\times 4$ and the corresponding Lanczos diagonalization
result is therefore close to the exact result in the thermodynamic limit.
