Not evaluated
Gaussian fields and SLE interfaces for Lipschitz heights (family 232)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, 3 manuscripts dated October 6, 2026 on Lipschitz heights and their Gaussian free-field limits.
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-232-gaussian-fields-sle-interfaces-lipschitz-r1
@misc{discoveria-oai-fam-232-gaussian-fields-sle-interfaces-lipschitz-r1,
author = {{DiscoverIA}},
title = {Gaussian fields and SLE interfaces for Lipschitz heights (family 232)},
howpublished = {DiscoverIA registry, entry oai-fam-232-gaussian-fields-sle-interfaces-lipschitz},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-232-gaussian-fields-sle-interfaces-lipschitz#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 Lipschitz height is a height whose variation between two points stays bounded by a constant times their distance. If the manuscripts were correct, the first two would give Gaussian free-field limits for integer Lipschitz heights; the third would concern uniform real Lipschitz surfaces on the triangular lattice.
What remains unclear
No Lean proof (Lean is a language in which a computer checks every step of a proof) is supplied for this family, and no third-party assessment is recorded. According to history.md, the 3 manuscripts were revised on October 7, 2026, the third to repair several of its arguments.
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 · Gaussian-free-field…link only, reading not recorded
- Repositorygithub.com · The-Gaussian-free-field…link only, reading not recorded
- Repositorygithub.com · Uniform-real-Lipschitz…link only, reading not recorded
Method
The openai/math repository contains 3 manuscripts: “Gaussian free-field limits of weighted integer Lipschitz heights”, “The Gaussian free field limit of integer Lipschitz heights with two-arc boundary data” and “Uniform real Lipschitz surfaces on the triangular lattice”. history.md describes the revision of the first as “supplies the annulus proof of the circuit estimate used in the discrete argument”. The absence of Lean is read from the absence of lean/docs/232.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: “Not all have accompanying Lean formalizations.”).
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 (Probability and statistical mechanics)
- In openai/math
- family 232, section “Probability and statistical mechanics”, 3 manuscripts dated Oct 6, 2026
- Lean proof
- none supplied
- Checked by
- no verifier identified
- Sources
- 4 : 4 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 226 of 372, by family number
- Not evaluated : Sharp three- and four-state reconstruction thresholds (family 229)
- Not evaluated : Exact Hausdorff measure for SLE (family 230)
- Not evaluated : The free uniform spanning forest is a factor of IID (family 231)
- Not evaluated : Gaussian fields and SLE interfaces for Lipschitz heights (family 232)
- Not evaluated : The joint critical Ashkin–Teller scaling limit (family 233)
- Not evaluated : All-temperature pressure for orthogonally invariant Ising spin glasses (family 234)
- Not evaluated : Random-SAT thresholds, sharp variance and computability (family 235)
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