Turán's distance-two conjecture for irreducible integer polynomials

Let $f(x)\in\mathbb{Z}[x]$ have degree $n\geq 1$. Define $L(f-g)=\sum_{j=0}^{n}|b_j-a_j|$ when $f(x)=\sum_{j=0}^{n}a_jx^j$ and $g(x)=\sum_{j=0}^{n}b_jx^j$. Turán's distance-two conjecture. There is an irreducible polynomial $g(x)\in\mathbb{Z}[x]$ of degree at most $n$ satisfying

$$L(f-g)\leq 2.$$

This is the integer-polynomial version of Turán's problem on approximating every polynomial by an irreducible polynomial with bounded coefficient distance. The existence of an absolute bound is connected to an open covering-system problem, and the distance-two assertion is presented as a conjecture; its resolution is not specified here.