Spectral Hierarchy of the Cosmic Web

The paper presents a spectral hierarchy for classifying the cosmic web by applying scale-weighting kernels to the density field before using eigenvalue-based methods. This framework unifies existing web definitions—potential/tidal, curvature-based, and higher-derivative levels—into a single, interpretable hierarchy that captures structure from large to small scales. The authors quantify the hierarchy’s information content by correlating a web contrast field with halo distributions, showing that it retains significant tracer-relevant information across scales, especially at nonlinear levels.

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