TMF-valued TQFT conjecture for four-dimensional invariants

Let $\mathcal{Z}$ denote the invariants of closed 3- and 4-manifolds and the proposed maps associated to cobordisms, valued in modules over $\operatorname{TMF}$. TMF-valued TQFT conjecture. These invariants give rise to a $(3+1)$-dimensional TQFT valued in modules over the ring spectrum $\operatorname{TMF}$. The construction is currently partial: the proposed cobordism maps still require extensions and further functoriality, so the existence of the full TQFT remains open.