At the height of the roman empire, how far north did the empire stretch?

The Roman Empire, during its peak, went as far north as Britannia. It took the regions of Londinium and Eboracum and went passed them. It was around AD 117 when the Roman Empire reached its greatest extend. After Trajan's death, many provinces were abandoned.

the doctrine of nullification recommended that states living inside the union have the one-sided, inalienable ideal to void any law made by the national government that could be esteemed illegal.

the united states was shaped based on a general agreement among its individual states. hence, it is inferred that under the hypothesis of invalidation, since the states are the establishment of the union, they have the ability to referee and disprove unlawful laws.