The super matrix factorization version of the Hodge conjecture

Let a supermanifold be described by a matrix-factorization category, and let its Jacobian ideal be viewed inside Hochschild cohomology. A $(p,p)$ class is a Hodge-type class of bidegree $(p,p)$ in this setting, and the category of singularities is the associated singularity category. Super matrix factorization Hodge conjecture. Every $(p,p)$ class in the Jacobian ideal (Hochschild cohomology) acts nontrivially on the category of singularities. This is proposed as a categorical analogue of the Hodge conjecture for supermanifolds; the supplied text does not state which cases are known or whether the claim has been resolved.