Epiphany as a Universal Manifold Transition

Epiphany as a Universal Manifold Transition presents a unified geometric theory of sudden insight, arguing that epiphany is not a psychological anomaly but a structural event that occurs across cognitive, cultural, developmental, physical, and formal manifolds. The paper defines manifolds as continuous spaces with local flatness and global curvature, where coherence, reachability, and identity are governed by gradients, boundaries, and density. Epiphany arises when curvature becomes sufficient to carry a system across a boundary into a denser region of coherence, reorganizing reachability and stabilizing a new orientation. The manuscript develops the geometry of curvature, boundaries, density, recognition, movement, and stabilization, and demonstrates their neural correlates through fMRI signatures of reconfiguration and integration. It identifies invariant conditions for manifold transitions, explains forced transitions into sparsity, and situates epiphany within a broader ontology of cognitive transformation. The result is a general structural account of insight, coherence, and reorientation across domains.