Usefulness of regularity slack diagrams on real data

Investigate whether regularity slack diagrams derived from filtered-link obstruction modules provide useful information on real-world data beyond their demonstrated ability to distinguish deliberately constructed synthetic families.

Background

The paper introduces regularity persistence and regularity slack diagrams to record how far a generator’s filtration value can move without changing persistent homology. A controlled experiment shows that slack summaries distinguish synthetic graph families designed with different local obstruction mechanisms.

The paper does not establish whether these descriptors have meaningful utility for real data analysis, leaving their practical informational value unresolved.

References

For the regularity descriptors, the open question is whether slack diagrams carry useful information on real data; our experiment only shows that they separate synthetic families built to differ.

— Homological Trimming and Regularity of Filtrations via Local Obstruction Modules  (2609.28160 - Pritam, 23 Sep 2026) in Section 8, subsection “Other generators and descriptors”