The supermanifold Hodge numbers and singularity-category gaps conjecture

Consider supermanifolds, their Hodge numbers, and the associated categories of singularities. A gap is a missing interval in the generation-time spectrum of such a category, and a missing supermanifold Hodge number is a Hodge number absent from the corresponding supermanifold Hodge data. Supermanifold gap correspondence conjecture. There is a correspondence between missing supermanifold Hodge numbers and increasing gaps of categories of singularities. The claim is intended to relate Hodge-theoretic defects of supermanifolds to categorical generation phenomena, but the supplied text gives no precise definition of the correspondence or evidence of resolution.