Not evaluated
Integral density on curve character varieties (family 027)
The gist
On October 6, 2026, OpenAI released a manuscript from an unreleased internal model on integral points of character varieties of curves, with a Lean formalisation.
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-027-integral-density-curve-character-varieties-r1
@misc{discoveria-oai-fam-027-integral-density-curve-character-varieties-r1,
author = {{DiscoverIA}},
title = {Integral density on curve character varieties (family 027)},
howpublished = {DiscoverIA registry, entry oai-fam-027-integral-density-curve-character-varieties},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-027-integral-density-curve-character-varieties#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
An integral point is a point whose coordinates are integers. If the manuscript were correct, it would bring a result on the integral points of these varieties; the sources read do not give its precise statement.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone and carries the label “unchecked”. No third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 027.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 · Integral-points-on…link only, reading not recorded
- Lean proofgithub.com · 027.mdpage read word for word
- Lean proofgithub.com · CharacterVarietiesAllSeams…link only, reading not recorded
Method
In the openai/math repository, family 027 comprises one manuscript, "Integral points on character varieties of curves" (dated September 25, 2026). The file lean/docs/027.md describes the scope of the formalisation: one Comparator statement, in lean/ComparatorChallenges/CharacterVarietiesAllSeamsSupport.lean. No revision of the manuscript is reported in history.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: “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 (Number theory)
- In openai/math
- family 027, section “Number theory”, 1 manuscript dated Sep 25, 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 27 of 372, by family number
- Not evaluated : An asymptotic formula for the number of totients (family 024)
- Not evaluated : Erdős’s short Egyptian-fraction conjecture (family 025)
- Not evaluated : Positive lower density of large prime gaps (family 026)
- Not evaluated : Integral density on curve character varieties (family 027)
- Not evaluated : The Gaussian moat conjecture (family 028)
- Not evaluated : Artin's primitive root conjecture: infinitude for every base (family 029)
- Not evaluated : Modularity over imaginary quadratic fields (family 030)
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