Measuring and Decomposing Mode Separation via the Canonical Diffusion

ArXi:2605.08777v1 Announce Type: cross Mode separation, namely how sharply a distribution fragments into barrier-separated clusters, is a fundamental geometric property of densities, difficult to quantify in high dimensions. It is structurally distinct from dispersion, yet existing tools fall short: differential entropy rises with spread regardless of fragmentation, PCA orders directions by variance regardless of barriers, and mutual information requires a mixture decomposition one usually does not have.