Not evaluated
Donaldson's tamed-to-compatible conjecture (family 342)
The gist
On October 6, 2026, OpenAI announced a new result on Donaldson's tamed-to-compatible conjecture, from an unreleased internal model.
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-342-donaldsons-tamed-compatible-conjecture-r1
@misc{discoveria-oai-fam-342-donaldsons-tamed-compatible-conjecture-r1,
author = {{DiscoverIA}},
title = {Donaldson's tamed-to-compatible conjecture (family 342)},
howpublished = {DiscoverIA registry, entry oai-fam-342-donaldsons-tamed-compatible-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-342-donaldsons-tamed-compatible-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscript were correct, it would bring a new result on this conjecture, which OpenAI's repository files under differential geometry. By its title, the statement concerns four-manifolds.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself and carries the mark “unchecked” in formalization.yaml; no third-party verification is recorded. The manuscript was revised on October 7, 2026, and the sources read do not say whether this revision changes the announced result.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 342.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 · Taming-implies…link only, reading not recorded
- Lean proofgithub.com · 342.mdpage read word for word
- Lean proofgithub.com · TamingCompatibility.leanlink only, reading not recorded
Method
The manuscript “Taming implies compatibility on four-manifolds” is dated October 6, 2026; the Lean supplied comprises lean/docs/342.md, one Comparator statement, and the file lean/ComparatorChallenges/TamingCompatibility.lean. According to history.md (October 7, 2026), the revision characterises the compatible cone by intersection positivity, restricts the cone-sum equality to a specific case, and adds a four-torus example in which an inclusion is strict. For formalization.yaml: family present in the “sources”. 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 (Differential geometry)
- In openai/math
- family 342, section “Differential geometry”, 1 manuscript dated Oct 6, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- 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 336 of 372, by family number
- Not evaluated : Katok's entropy rigidity conjecture (family 339)
- Not evaluated : Counterexample to the nearby Lagrangian conjecture (family 340)
- Not evaluated : Donaldson's hypersymplectic deformation conjecture (family 341)
- Not evaluated : Donaldson's tamed-to-compatible conjecture (family 342)
- Not evaluated : Sharp symplectic ball-packing criteria in higher dimensions (family 343)
- Not evaluated : The metric Blaschke conjecture (family 344)
- Not evaluated : Infinitely many closed geodesics on spheres and three-manifolds (family 345)
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