A declaration without a penalty is an opinion. Paul III appears to have understood that, because on 29 May 1537, days before the bull, he issued a brief called Pastorale Officium, addressed to the Cardinal Archbishop of Toledo, which attached automatic excommunication to anyone who enslaved the peoples of the Indies or seized their goods. That brief is the enforcement that Sublimis Deus lacks.
The Spanish crown objected. It held the right of patronage over the church in its American possessions and regarded a papal penalty imposed directly on its subjects, without passing through the royal council, as an intrusion on that right. The objection was jurisdictional rather than doctrinal, and it succeeded. On 19 June 1538 Paul III annulled Pastorale Officium.
The result is an instrument in two halves with different fates. The declaration survives, is quoted in every account of the sixteenth century debate, and was invoked by Bartolome de las Casas for the rest of his life. The sanction lasted a year. Slavery of indigenous Americans continued under changed legal forms, and the Atlantic traffic in enslaved Africans, which the bull does not address at all, expanded through the same century. Reading the declaration without the annulment produces a much better story than the record supports, which is why the atlas carries both dates.