Comparison for rigid but non-projectively rigid algebras

Determine whether the comparison theorem identifying the telescope conjecture with the corresponding statement for the heart remains valid for rigid algebras that are not necessarily projectively rigid.

Background

The paper proves that, for projectively rigid algebras, atomic smashing ideals and the telescope conjecture are detected on the heart. It explicitly asks whether this result extends to the broader class of rigid algebras.

References

Does \cref{comparisontcinc} work for any rigid (but not necessarily projectively rigid) -algebra?

— Generalized Telescope Conjecture  (2609.03375 - Liang, 3 Sep 2026) in Section 7, subsection “Smashing frames of additive $\infty$-categories”