Spectral Concentration at the Edge of Stability: Information Geometry of Kernel Associative Memory

High-capacity kernel Hopfield networks exhibit a $\mathit{\text{Ridge}}\mathit{\text{of}}\mathit{\text{Optimization}}$ characterized by extreme stability. While previously linked to $\mathit{\text{Spectral}}\mathit{\text{Concentration}}$, its origin remains elusive. Here, we analyze the network dynamics on a statistical manifold, revealing that the Ridge corresponds to the Edge of Stability, a critical boundary where the Fisher Information Matrix becomes singular. We demonstrate that the apparent Euclidean force antagonism is a manifestation of $\mathit{\text{Dual}}\mathit{\text{Equilibrium}}$ in the Riemannian space. This unifies learning dynamics and capacity via the Minimum Description Length principle, offering a geometric theory of self-organized criticality.