OpenAI · 118-01 · 2026-09-24 · Theoretical computer science
Additive hardness and unbounded configuration gaps in bin packing
preprints/Additive-hardness-and-unbounded-configuration-gaps-in-bin-packing-September-24-2026
Family 118. Unbounded bin-packing gaps and the modified integer round-up conjecture.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Disproves the modified integer round-up conjecture of Scheithauer and Terno: the integral bin-packing optimum can exceed its configuration linear-programming value by an arbitrarily large additive constant. Approximating the optimum within any fixed additive constant is also NP-hard, even when every item exceeds and each bin holds at most five items.
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 bins is NP-hard. Both results hold with rational item sizes greater than 1/6, so each bin contains at most five items.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
This preprint is named in the Lean scope note for 118: Bin packing and unbounded configuration-LP gaps. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.