Trialgebra reconstruction conjecture for quantum groups and Donaldson–Floer theory

A trialgebra is an algebraic structure with three compatible algebraic operations, as envisioned here for constructing four-dimensional topological quantum field theories. Trialgebra reconstruction conjecture. There exists a family of trialgebras from whose representations the quantum groups can be recovered. It is also possible to reproduce Donaldson–Floer theory from them. This conjecture proposes that trialgebras provide an algebraic foundation for four-dimensional topological quantum field theories, analogous to the roles of monoidal bicategories and Hopf categories in lower-dimensional constructions. The paper does not establish the existence of such a family or the claimed reconstruction.