ArrowSpace is a library that implements a novel spectral indexing approach for vector similarity search, combining traditional semantic similarity with graph-based spectral properties. The library introduces taumode (λτ , lambda-tau) indexing, which blends Rayleigh quotient smoothness energy from graph Laplacians with edge-wise dispersion statistics to create bounded, comparable spectral scores. This enables similarity search that considers both semantic content and spectral characteristics of high-dimensional vector datasets.