The fixed--modular integer programming tractability conjecture

Let $\Delta \in \mathbb{Z}_{>0}$ be fixed. An integer program of the form (IP) has a constraint matrix $B$ that is $\Delta$-modular if its full-rank minors have absolute value at most $\Delta$ and at least one has absolute value $\Delta$.

Fixed-$\Delta$ tractability conjecture. There is a polynomial-time algorithm to solve any integer program of the form (IP) with a $\Delta$-modular constraint matrix.

This conjecture extends the polynomial-time solvability of totally unimodular integer programs to every fixed bound on the maximal non-vanishing subdeterminants. Its status is not resolved in the supplied text.