Not evaluated
The Euclidean Steinitz–Bergström conjecture (family 097)
The gist
In its release of October 6, 2026, OpenAI presents, using an unreleased internal model, a manuscript on the Euclidean Steinitz–Bergström theorem.
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-097-euclidean-steinitzbergstrom-conjecture-r1
@misc{discoveria-oai-fam-097-euclidean-steinitzbergstrom-conjecture-r1,
author = {{DiscoverIA}},
title = {The Euclidean Steinitz–Bergström conjecture (family 097)},
howpublished = {DiscoverIA registry, entry oai-fam-097-euclidean-steinitzbergstrom-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-097-euclidean-steinitzbergstrom-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The manuscript concerns the Euclidean version, the one using the usual distance, of the Steinitz–Bergström theorem. This theorem belongs to a wider setting: reordering vectors that sum to zero so that all the partial sums stay close to the origin. The announced result would fit within it, going by its title.
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, and the sources read give only the manuscript's title, not its statement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 097.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 · The-Euclidean-Steinitz…link only, reading not recorded
- Lean proofgithub.com · 097.mdpage read word for word
- Lean proofgithub.com · SteinitzBergstrom.leanlink only, reading not recorded
Method
The openai/math repository contains the manuscript “The Euclidean Steinitz–Bergström theorem”, dated September 24, 2026, and the file lean/docs/097.md, which describes the Lean formalisation with one Comparator statement (lean/ComparatorChallenges/SteinitzBergstrom.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
- Mathematics (Convex and metric geometry)
- In openai/math
- family 097, section “Convex and metric geometry”, 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 94 of 372, by family number
- Not evaluated : Subpolynomial dimension reduction in L_p (family 094)
- Not evaluated : Hyperbolicity cones without semidefinite lifts (family 095)
- Not evaluated : The Gaussian propeller conjecture (family 096)
- Not evaluated : The Euclidean Steinitz–Bergström conjecture (family 097)
- Not evaluated : A negative answer to the Lang–Plaut problem (family 098)
- Not evaluated : The sharp distortion of edit distance into ℓ_1 (family 099)
- Not evaluated : A counterexample to Bang's cylinder-covering bound (family 100)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.