This crystalline dodecahedron pulses with self-writing equations that shift and evolve across its faceted surfaces, displaying probability matrices that glow with varying intensities based on dimensional stability. Mathematical symbols phase in and out of existence around its core, while geometric patterns reconfigure themselves to match the current state of cross-realm magical interactions. The artifact resonates with harmonic frequencies when its equations achieve temporary balance, creating a sound that stabilizes nearby rift energies.

The Chaos Theorem serves as the mathematical foundation underlying all stable magical interactions within the Arcane Fracture, continuously calculating the precise conditions needed to prevent reality collapse during volatile cross-league convergences.