1: [Nexus Nucleus 01]
The Nucleus resides at the very center of the Magical Nexus - the intersection of multiple worlds and whims. Another of the Stair Shaper's creations, this Structure serves as a conduit of the Magical energies that accumulate as more Monsters are Transposed to the Nexus. It's able to accomplish this by absorbing their energy signatures and converting them into a tangible form. If its shape looks familiar, that's because the diverse Star Rocks of the Monster World are actually the Stair Shaper's handiwork as well; left behind as monuments to 'first contact' and obtainable only through Starpower, the essence that amasses when harmonies from differing worlds are sung.
2: [Nexus Nucleus 02 - Augmented]
Just as a chord in music theory can be 'augmented,' so too can the Magical Nexus's Nucleus Structure. This is accomplished with a technique akin to (but not exactly like) Transposition - one major difference is that the augmentation requires Shards, which we thought could only be produced in the pocket dimension... and rather than 'lifting' the whole item, only part of it gets lifted... ?.. it gets kind of complicated to explain (this is true of music theory in general), so perhaps it's better to just smile and nod. The important thing you need to know is that the Structure's ability to display unified Monster populations with glowing Rhombi is still intact - now with extra sparkles. Who doesn't like sparkles?