Not evaluated
A stable-coordinate counterexample in four variables (family 049)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a counterexample in four variables: a “stable coordinate” that is not a coordinate.
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-049-stable-coordinate-counterexample-four-r1
@misc{discoveria-oai-fam-049-stable-coordinate-counterexample-four-r1,
author = {{DiscoverIA}},
title = {A stable-coordinate counterexample in four variables (family 049)},
howpublished = {DiscoverIA registry, entry oai-fam-049-stable-coordinate-counterexample-four},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-049-stable-coordinate-counterexample-four#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
A polynomial is a “coordinate” if it can serve as a variable after a polynomial change of variables; it is “stable” if this holds once extra variables are added. If the counterexample held, it would show that in four variables, being a stable coordinate does not imply being a coordinate.
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 carries the label “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 · 049.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-stable-coordinate-that…link only, reading not recorded
- Repositorygithub.com · An-explicit-noncoordinate…link only, reading not recorded
- Lean proofgithub.com · 049.mdpage read word for word
- Lean proofgithub.com · AbhyankarSathaye.leanlink only, reading not recorded
- Lean proofgithub.com · CommutingDerivations.leanlink only, reading not recorded
- Lean proofgithub.com · StableCoordinateFour.leanlink only, reading not recorded
Method
In the openai/math repository, family 049 comprises two manuscripts: "A stable coordinate that is not a coordinate in four variables" (dated October 5, 2026) and "An explicit noncoordinate polynomial with affine three-space zero fibre" (dated September 24, 2026). The file lean/docs/049.md describes the scope of the formalisation: three Comparator statements, in lean/ComparatorChallenges/AbhyankarSathaye.lean, lean/ComparatorChallenges/CommutingDerivations.lean and lean/ComparatorChallenges/StableCoordinateFour.lean. No revision is reported in history.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 (Algebraic and complex geometry)
- In openai/math
- family 049, section “Algebraic and complex geometry”, 2 manuscripts 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
- 7 : 1 read word for word, 6 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 48 of 372, by family number
- Not evaluated : Counterexamples to Shafarevich holomorphic convexity (family 046)
- Not evaluated : Complex counterexamples to cancellation and affine fibrations (family 047)
- Not evaluated : A characteristic-zero counterexample to Lipman–Zariski (family 048)
- Not evaluated : A stable-coordinate counterexample in four variables (family 049)
- Not evaluated : A counterexample to Griffiths' positivity conjecture (family 050)
- Not evaluated : Kobayashi's canonical-ampleness conjecture (family 051)
- Not evaluated : Tangent-bundle splittings and universal covers (family 052)
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.