Determine whether uncountable-cosumpact objects in stable infinity-categories vanish

Determine whether every -kappa-cosumpact object in a presentable stable -infinity-category is zero for every uncountable regular cardinal -kappa.

Background

The paper proves that every cosumpact object in a presentable stable -infinity-category is zero, using the main theorem together with the relationship between compactness and sumpactness in stable settings. This settles the unindexed, or -aleph_0, case.

The authors explicitly leave open the analogous assertion for -kappa-cosumpact objects at uncountable regular cardinals. A positive answer would extend the vanishing result and would further constrain copresentability phenomena for presentable stable -infinity-categories.