Hardness for application-derived distributions

Establish average-case hardness results for Betti-number estimation comparable to those obtained under the balanced planted-clique distribution for probability distributions arising from practical applications.

Background

The balanced planted-clique distribution is selected because it directly supports the reduction from planted-clique detection, but the paper explicitly disclaims that it is a statistical model for typical TDA data. The unresolved problem is therefore to transfer comparable hardness guarantees to distributions motivated by biological, medical, financial, or other applied data.

References

It remains open to establish comparable hardness results for distributions arising in applications.

— Average-case hardness of Betti number estimation  (2609.12777 - Strelchuk et al., 11 Sep 2026) in Section 1, paragraph “The importance of the distribution choice”