Equivalence between MM++ and supercompact Laver-genericity

Investigate whether there exists a reasonable set-theoretic assumption under which Martin’s Maximum++ is equivalent to the existential axiom asserting the existence of a tightly P-Laver-generically supercompact cardinal for some iterable class P of posets.

Background

The paper shows that MM++ together with a proper class of supercompact cardinals can be made consistent with GA, whereas various Laver-generic large cardinal assumptions often yield ¬GA. Bridging these frameworks by an equivalence would be a significant unification.

The problem seeks conditions under which the combinatorial forcing axiom MM++ and the large-cardinal-style assertion of supercompact Laver-genericity coincide, potentially guided by results of Woodin and later refinements.