The approximation scheme of the fifth theorem from the profile sweep: read the word, zero the weights of the jobs that cannot be preprocessed on their own, choose the rescaling $k$, round the weights up to multiples of $k$, run the profile sweep of the third theorem with the threshold $2 e n²$ that the rounding leaves, and write $k · (W' - n)$, where $W'$ is the largest weight the rescaled table reaches ($W'$ itself when $k = 1$).