A weighted angle distance on strings

We define a multi-scale metric $d_{\rho }$ on strings by aggregating angle distances between all $n$-gram count vectors with exponential weights ${\rho }^n$. We benchmark $d_{\rho }$ in DBSCAN clustering against edit and $n$-gram baselines, give a linear-time suffix-tree algorithm for evaluation, prove metric and stability properties (including robustness under tandem-repeat stutters), and characterize isometries.