Abstract.

We introduce the concept of homorupt—a homotopy rupture where continuous transformation between representation spaces breaks down catastrophically. When language models elaborate token-space patterns beyond critical thresholds, the topological invariants connecting representations to ground truth cannot be preserved.

The result is a system that appears coherent locally but has lost all genuine logical connection to its referent domain. This paper formalizes the conditions under which representational fidelity collapses and explores the implications for AI systems claiming to model social, linguistic, or conceptual reality.

We establish connections to Whitney stratifications, Goresky's geometric cocycles, and Coulon compactification theory, providing rigorous criteria for detecting and preventing representational catastrophe.