The poem is a sequence of instructions, and its order matters. It begins with obligations outward: the gods, the oath, parents, kin, friends, and the ranking of them. It moves to the government of the self, telling the reader to master appetite and anger and to weigh a course before acting on it. It then gives the practice the poem is best known for, the review of the day before sleep, in which the reader asks what was done, what was left undone, and what was done wrongly. Only at the end does it turn to what lies beyond the moral life. That structure makes it a rule rather than a doctrine.
There is no metaphysics argued in it and no cosmology, and the transmigration and purification the closing lines assume are stated rather than demonstrated. It works as something to be memorised and applied, which is how a school hands on a way of living rather than a set of propositions. The verses circulated as a school text for that reason, in a form short enough to hold in the memory whole and plain enough to be recited without a commentary. Their appeal outlasted the school that produced them: readers with no Pythagorean commitments at all, from late antique Platonists to Renaissance humanists to modern esoteric orders, have taken them up as a moral handbook, and the daily examination in particular has been borrowed repeatedly by traditions with no interest in the rest.