Not evaluated
Tangent-bundle splittings and universal covers (family 052)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, two manuscripts on splittings of the tangent bundle of compact Kähler manifolds and of rationally connected manifolds.
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-052-tangent-bundle-splittings-universal-covers-r1
@misc{discoveria-oai-fam-052-tangent-bundle-splittings-universal-covers-r1,
author = {{DiscoverIA}},
title = {Tangent-bundle splittings and universal covers (family 052)},
howpublished = {DiscoverIA registry, entry oai-fam-052-tangent-bundle-splittings-universal-covers},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-052-tangent-bundle-splittings-universal-covers#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 manuscripts were correct, they would establish, going by their titles, results on the splitting of the tangent bundle (the set of possible directions at each point of a geometric space): one on the universal cover, the unfolded version of the space, of a compact Kähler manifold, the other on the integrability of a split tangent bundle. The repository files this family under the section “Algebraic and complex geometry”.
What remains unclear
No check of the Lean supplied by OpenAI (a language in which a computer checks every step of a proof) by a third party, nor any other independent assessment, is recorded. The sources read do not detail how much of the two manuscripts the Lean covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 052.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 · Universal-cover-splitting…link only, reading not recorded
- Repositorygithub.com · Integrability-of-split…link only, reading not recorded
- Lean proofgithub.com · 052.mdpage read word for word
- Lean proofgithub.com · KahlerSplitting.leanlink only, reading not recorded
- Lean proofgithub.com · SplitTangentIntegrability.…link only, reading not recorded
Method
The two manuscripts in the openai/math repository are “Universal-cover splitting for compact Kähler manifolds” and “Integrability of split tangent bundles on rationally connected manifolds”, dated September 23, 2026. OpenAI supplies lean/docs/052.md and two Lean files (two Comparator statements), lean/ComparatorChallenges/KahlerSplitting.lean and lean/ComparatorChallenges/SplitTangentIntegrability.lean; formalization.yaml carries “review: status: unchecked” and lists the family in its sources. history.md reports no revision of these manuscripts. 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 052, section “Algebraic and complex geometry”, 2 manuscripts dated Sep 23, 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
- 6 : 1 read word for word, 5 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 51 of 372, by family number
- 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)
- Not evaluated : A counterexample to Pixton's original completeness conjecture (family 053)
- Not evaluated : Counterexamples to Kuznetsov's rationality conjecture (family 054)
- Not evaluated : Toda's Gepner conjecture and large-volume stability (family 055)
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