Lipschitz top-n truncation for persistence diagrams

Construct a genuinely 1-Lipschitz replacement for top-$N$ persistence-bar truncation under the bottleneck metric, while retaining a computationally manageable representation for the COMPLEX embedding.

Background

The implementation retains only the 50 most persistent bars in each slice. The paper notes that this truncation is not 1-Lipschitz for the bottleneck metric, so the stated guarantees apply to the truncated fibered barcode rather than automatically to the untruncated module. A soft truncation that is genuinely 1-Lipschitz would remove this gap and provide a cleaner stability relationship between the computed descriptor and the full persistence information.

References

A soft, genuinely $1$-Lipschitz alternative to top-$n$ is the clean fix and we leave it open.

— COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules  (2609.22012 - Majhi et al., 18 Sep 2026) in Remark 2.3, “What the guarantees are about”