Not evaluated
Unbounded bin-packing gaps and the modified integer round-up conjecture (family 118)
The gist
In its release of October 6, 2026, OpenAI announces, using an unreleased internal model, unbounded configuration gaps for the bin packing problem.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-118-unbounded-bin-packing-gaps-modified-integer-r1
@misc{discoveria-oai-fam-118-unbounded-bin-packing-gaps-modified-integer-r1,
author = {{DiscoverIA}},
title = {Unbounded bin-packing gaps and the modified integer round-up conjecture (family 118)},
howpublished = {DiscoverIA registry, entry oai-fam-118-unbounded-bin-packing-gaps-modified-integer},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-118-unbounded-bin-packing-gaps-modified-integer#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Bin packing consists of putting objects of given sizes into boxes of the same capacity. If the manuscript held, the configuration gaps (a technical notion of this problem) would not be bounded by any constant.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file marks it as unchecked. No third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 118.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Additive-hardness-and…link only, reading not recorded
- Lean proofgithub.com · 118.mdpage read word for word
- Lean proofgithub.com · BinPackingGap.leanlink only, reading not recorded
Method
The openai/math repository contains the manuscript “Additive hardness and unbounded configuration gaps in bin packing”, dated September 24, 2026, and the file lean/docs/118.md, which describes the Lean formalisation with one Comparator statement (lean/ComparatorChallenges/BinPackingGap.lean). The family is among the sources of formalization.yaml; history.md reports no revision of this manuscript. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Theoretical computer science
- In openai/math
- family 118, section “Theoretical computer science”, 1 manuscript dated Sep 24, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 4 : 1 read word for word, 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 115 of 372, by family number
- Not evaluated : Sampling and counting contingency tables with arbitrary margins (family 115)
- Not evaluated : Uniform identity testing for noncommutative formulas (family 116)
- Not evaluated : Uniform sparsest cut: hardness and semidefinite gaps (family 117)
- Not evaluated : Unbounded bin-packing gaps and the modified integer round-up conjecture (family 118)
- Not evaluated : The Courtade–Kumar and Hellinger conjectures (family 119)
- Not evaluated : Almost-linear-time exact matching in general graphs (family 120)
- Not evaluated : Almost-linear expected-time approximation of edit distance (family 121)
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