The reason the National Alchemy Academy started researching the topological alchemy array was due to their exploration of the Sea of Nightmares.
Because of the spacetime inversion, many alchemy arrays and alchemical items were unable to be used within it, which had great impact on researchers' daily lives and safety.
Under careful observation of researchers, some alchemists found that certain alchemy arrays could still operate when the spacetime inversion was occurring, whereas others couldn't.
After some experimentation, a Ring alchemist finally discovered the reason why some alchemy arrays could still function.
Under the impact of spacetime inversion, many alchemy arrays would undergo different degrees of deformation due to the bending of spacetime, and it was this deformation that caused them to fail to function properly.
However, the alchemy arrays that still managed to work had certain 'stable' structures to some degree.