The first statement is the running time of the greedy, on the slice of instances with equal preprocessing times and unit weights. Its bound is the sorting term alone, which is what the paper's $O(n \log n)$ says.

The second bullet has no running-time statement here, and that is deliberate. The $O(n^{2.5} L)$ the paper quotes is the running time of a particular linear programming algorithm, cited and not proved there, and the route from total unimodularity to an integral optimum is the theorem of Hoffman and Kruskal, also cited. A running-time statement for this case would therefore rest on two results from outside, neither of them available in the background library, and asserting it would say nothing this submission could support.

What Section 6.2 does establish is stated in full elsewhere, and proved: the scheduling problem is that integer program ($Lemma5.ilp_correct$, $Lemma5.ilp_optimum$), its constraint matrix has the consecutive ones property on a proper instance ($Lemma5.lemma5$), and such a matrix is totally unimodular ($Lemma5.matrix_isTotallyUnimodular$, via $ConsecutiveOnes.isTotallyUnimodular$, which is proved rather than assumed). That is the mathematical content of the bullet; the step from it to a running time is the citation.

The statement that remains is about the decision problem with a threshold, as the others are, so that the whole submission speaks about one problem.

The domain also asks that every processing time be positive, $q_j \ge 1$. This is the paper's standing assumption for the recursions behind the algorithms — a job with $q_j = 0$ has an empty second operation, and the characterization of the feasible sets, on which everything rests, is stated for jobs that have a genuine one — but the paper does not repeat it in each claim, and a statement about a program that reads an arbitrary word has to.