This artifact manifests as a translucent crystalline disc inscribed with ever-shifting mathematical formulae that pulse with the combined colors of all ten realms. The equations continuously rewrite themselves in response to magical fluctuations, creating harmonic frequencies that resonate across dimensional boundaries. When cross-realm events occur, the theorem generates stabilizing field equations that prevent catastrophic magical interference while enabling controlled energy exchange between incompatible schools.

The Binding Theorem serves as both the fundamental law governing inter-realm stability and an active guardian against magical apocalypse, automatically adjusting the mathematical relationships between conflicting energies to maintain dimensional integrity during cross-league events.