Not evaluated
A negative answer to the Lang–Plaut problem (family 098)
The gist
On October 6, 2026, OpenAI released a manuscript claiming a “doubling” subset of Hilbert space with no bi-Lipschitz embedding in finite dimension.
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-098-negative-answer-langplaut-problem-r1
@misc{discoveria-oai-fam-098-negative-answer-langplaut-problem-r1,
author = {{DiscoverIA}},
title = {A negative answer to the Lang–Plaut problem (family 098)},
howpublished = {DiscoverIA registry, entry oai-fam-098-negative-answer-langplaut-problem},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-098-negative-answer-langplaut-problem#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript held, it would provide a subset of Hilbert space (a space with any number of dimensions) that would be “doubling”. This means that every ball can be covered by a bounded number of balls half the size. The subset would have no bi-Lipschitz embedding in finite dimension, that is, no copy in a finite-dimensional space that distorts distances by at most a constant factor.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and the repository marks its review “unchecked”. No third-party verification is recorded. The manuscript comes from an internal model that OpenAI has not released.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 098.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 · A-doubling-Hilbert-subset…link only, reading not recorded
- Lean proofgithub.com · 098.mdpage read word for word
- Lean proofgithub.com · CompactBanach.leanlink only, reading not recorded
- Lean proofgithub.com · DoublingHilbert.leanlink only, reading not recorded
Method
In the openai/math release, family 098 has a single manuscript, dated September 25, 2026: “A doubling Hilbert subset with no finite-dimensional bi-Lipschitz embedding”. It is filed under the section “Convex and metric geometry” of overview.tex; history.md reports no revision. OpenAI adds 2 Lean Comparator files, lean/ComparatorChallenges/CompactBanach.lean and lean/ComparatorChallenges/DoublingHilbert.lean, described in lean/docs/098.md. 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 098, section “Convex and metric geometry”, 1 manuscript dated Sep 25, 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
- 5 : 1 read word for word, 4 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 95 of 372, by family number
- 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)
- Not evaluated : The sharp simplex conjecture for isotropic constants (family 101)
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