Not evaluated
Interior C^(1,α) regularity for infinity-harmonic functions (family 377)
The gist
On October 6, 2026, OpenAI published a manuscript on uniform interior C^(1,α) estimates for infinity-harmonic functions, 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-377-interior-c-1-alpha-regularity-infinity-r1
@misc{discoveria-oai-fam-377-interior-c-1-alpha-regularity-infinity-r1,
author = {{DiscoverIA}},
title = {Interior C^(1,α) regularity for infinity-harmonic functions (family 377)},
howpublished = {DiscoverIA registry, entry oai-fam-377-interior-c-1-alpha-regularity-infinity},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-377-interior-c-1-alpha-regularity-infinity#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
A function is of class C^(1,α) when it is continuously differentiable and its derivative varies in a controlled way. For any two points, the gap between the values of the derivative is at most a constant times their distance raised to the power α, fixed above zero and at most one. If the manuscript were correct, it would give estimates of this kind in the interior of the domain of the functions studied.
What remains unclear
The sources read specify neither the value of α nor with respect to what the estimates are “uniform”. No Lean (a language in which a computer checks every step of a proof) is supplied, and the sources read report no third-party assessment.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.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 · Uniform-Interior-C1alpha…link only, reading not recorded
Method
The manuscript “Uniform Interior C^(1,α) Estimates for Infinity-Harmonic Functions”, dated October 4, 2026, is the only one of family 377 listed in CONTENTS.md of the openai/math repository. Its folder is named Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026. There is no lean/docs/377.md; the repository README states: “Not all have accompanying Lean formalizations.” history.md reports no revision. 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).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Partial differential equations)
- In openai/math
- family 377, section “Partial differential equations”, 1 manuscript dated Oct 4, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
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 370 of 372, by family number
- Not evaluated : Sharp one-third stability of optimal transport maps (family 374)
- Not evaluated : De Giorgi's conjecture in dimension eight (family 375)
- Not evaluated : Universal computation in forced Navier–Stokes flows (family 376)
- Not evaluated : Interior C^(1,α) regularity for infinity-harmonic functions (family 377)
- Not evaluated : Counterexample to Hadwiger's conjecture
- Withdrawn : Three manuscripts withdrawn after a sign error (Weil classes, Kuga–Satake K3, rational Hodge)
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