Not evaluated
A smooth surface metric with no local immersion in ℝ³ (family 334)
The gist
On October 6, 2026, OpenAI announced a manuscript dated September 24, 2026 claiming a smooth metric with no local isometric immersion into three-space.
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-334-smooth-surface-metric-no-local-immersion-r-3-r1
@misc{discoveria-oai-fam-334-smooth-surface-metric-no-local-immersion-r-3-r1,
author = {{DiscoverIA}},
title = {A smooth surface metric with no local immersion in ℝ³ (family 334)},
howpublished = {DiscoverIA registry, entry oai-fam-334-smooth-surface-metric-no-local-immersion-r-3},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-334-smooth-surface-metric-no-local-immersion-r-3#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 smooth metric on a surface is a way of measuring lengths on it. A local isometric immersion would place a small piece of the surface in three-dimensional space while preserving lengths. If the manuscript held, a metric being smooth would not be enough to guarantee such a realisation.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, with the wording “review: status: unchecked”. No third-party verification is read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 334.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-Smooth-Metric-with-No…link only, reading not recorded
- Lean proofgithub.com · 334.mdpage read word for word
- Lean proofgithub.com · IsometricImmersion.leanlink only, reading not recorded
Method
Manuscript of September 24, 2026: “A Smooth Metric with No Local Isometric Immersion into Three-Space”. The claimant supplies lean/docs/334.md and 1 Comparator file: lean/ComparatorChallenges/IsometricImmersion.lean. Section “Differential geometry”; family present in the sources of formalization.yaml; history.md records 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: “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 334, section “Differential geometry”, 1 manuscript 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
- 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 328 of 372, by family number
- Not evaluated : Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming (family 331)
- Not evaluated : Metric Markov cotype two for ℓ_1 (family 332)
- Not evaluated : Smooth isometric immersions of surfaces into ℝ⁴ (family 333)
- Not evaluated : A smooth surface metric with no local immersion in ℝ³ (family 334)
- Not evaluated : Gromov's integral scalar-curvature inequality (family 335)
- Not evaluated : Spectral scalar curvature and codimension-two width (family 336)
- Not evaluated : Cartan–Hadamard isoperimetry and CAT(0) fillings (family 337)
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