Lyra awoke in the center of a space that felt both infinite and perfectly folded, a manifold she soon recognized as T^3, the three-dimensional torus.

Suspended vertically in this strange, looping world was the Euler characteristic itself, glowing like a circle carved from pure light. It spun slowly, a submanifold of the torus, serene but pregnant with potential.

When Lyra first touched it, the Euler reacted—quivering like a bell—and she sensed that her journey had begun. The call came not as words but as a pulse that resonated through the loops of the torus, inviting her to venture beyond her ordinary understanding of space and structure.

Lyra awoke in the center of a space that felt both infinite and perfectly folded, a manifold she soon recognized as T^3, the three-dimensional torus. 

Suspended vertically in this strange, looping world was the Euler characteristic itself, glowing like a circle carved from pure light. It spun slowly, a submanifold of the torus, serene but pregnant with potential. 

When Lyra first touched it, the Euler reacted—quivering like a bell—and she sensed that her journey had begun. The call came not as words but as a pulse that resonated through the loops of the torus, inviting her to venture beyond her ordinary understanding of space and structure.