Additive hardness and unbounded configuration gaps in bin packing

We disprove the Modified Integer Round-Up Conjecture for bin packing by constructing instances with arbitrarily large additive gaps between the configuration-LP value and the integral optimum. We also prove that, for every fixed nonnegative integer $c$, distinguishing instances that fit in $B$ bins from those requiring more than $B+c$ bins is NP-hard. Both results hold with rational item sizes greater than $1/6$, so each bin contains at most five items.