Arcus Pactum (アルカス・パクトウム Arukasu Pakutoumu, lit. Arc of Covenant in Latin), or more commonly known as Contract of the Rainbow (契約の虹 Keiyaku no Niji) is the forbidden trademark spell of Georgius of the Rainbow. It is the ultimate spell that enabled him to imprison the immortal Witch of Babylon, Lieselotte Werckmeister.
From how it was used, Contract of the Rainbow is most likely a dimensional-affecting-spell. It has the ability to shatter reality of its target, greatly weakening or even killing the user's enemy off from reality. The use of Contract of the Rainbow, as stated by Shiori Momono, can cause the root of reality to be shattered beyond repair, which is perhaps the reason why it was forbidden in the first place.
Since it is a powerful spell, the user is almost guaranteed to face death right after execution. This drawback can be overcome by providing the user with an abundant amount of magical energy, however.
Quantum Physics Perspective
In Resona Forma, Johanna did an experiment and revealed the truth about Arcus Pactum's ability. She argues that scattering the fragments of Lieselotte to parallel dimensions is impossible, as parallel worlds are supposed to be equal in value, meaning that in each world, there will be a Lieselotte, thus it is pointless to scatter her fragments there. Furthermore, even if scattering was possible, it would be strange for Arcus Pactum to only spread them into seven worlds while there should be an infinite number of parallel worlds.
As common time-space knowledge is insufficient, Johanna applied her theory on the relationship between the world and God based on quantum physics to provide a different explanation. In her perspective, Arcus Pactum is simply an extremely powerful magical blast. However, its power is so great that the damage scale exceeds the range of physical limitation and reaches the Monads, the same composition of the world, of Lieselotte, causing them to be restructured. This causes God to lose his recognition of the target, and since only what He recognizes can exist in His world, Lieselotte disappeared.
- In the anime, the spell was used by all six members of the Black Knights to seal off Lieselotte; the price was that they had to take on their current grotesque forms.