External Hoyer–Mazur conjecture for bi-incomplete Tambara functors

Let $(\mathcal O_a,\mathcal O_m)$ be a compatible pair of indexing categories. An $\mathcal O_a$-Mackey functor is a Mackey functor with additive transfers restricted by $\mathcal O_a$, and an $\mathcal O_m$-commutative monoid is a commutative monoid whose multiplicative norms are restricted by $\mathcal O_m$.

External Hoyer–Mazur conjecture. For any compatible pair of indexing categories $(\mathcal O_a,\mathcal O_m)$, there is an equivalence of categories between $\mathcal O_m$-commutative monoids in $\mathcal O_a$-Mackey functors and $(\mathcal O_a,\mathcal O_m)$-Tambara functors.

This is proposed as an external, algebraic description of bi-incomplete Tambara functors, generalizing the characterization of ordinary Tambara functors as commutative monoids in Mackey functors. The source gives no resolution of the conjecture.