Higher semiadditive modes as smashing fields

Determine whether the m-semiadditive mode CMon_m(\mathcal{S}) is a smashing field for every integer m\geq -2.

Background

The paper defines a smashing field as a symmetric monoidal infinity-category whose frame of coidempotent objects has exactly two elements, and proves that smashing fields satisfy the telescope conjecture. The cases m\in[-2,0] are established, motivating the unresolved question for higher semiadditive modes.

References

Let $m\geq-2$ be an integer. Is the $m$-semiadditive mode $CMon_m()$ appearing in a smashing field? (We have shown that it holds when $m\in[-2,0]$.)

— Generalized Telescope Conjecture  (2609.03375 - Liang, 3 Sep 2026) in Section 4, subsection “Smashing fields”