Data-driven selection of the hierarchy step k

Develop a data-driven procedure to estimate the hierarchy step k from observed cascade data and to quantify the associated uncertainty within the framework of the hierarchical symmetry axiom A1.

Background

The theoretical development treats the hierarchy step k as known, which simplifies the formulation of A1 and the derivation of scaling exponents.

In applications, k is not known a priori and must be inferred from data. The authors identify the lack of a principled estimation and uncertainty quantification procedure for k as an outstanding task.

References

Several directions remain open. The hierarchy step~$k$ is treated as a given parameter. In applications, $k$~must be estimated from data; a data-driven procedure for selecting~$k$ and quantifying its uncertainty would be valuable.

— Hierarchical symmetry selects log-Poisson cascades: classification, uniqueness, and stability  (2604.01632 - Freeburg, 2 Apr 2026) in Section 6, Concluding remarks