Not evaluated
Single-fold Diophantine representations (family 242)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript dated September 24, 2026 on single-fold Diophantine representations.
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-242-single-fold-diophantine-representations-r1
@misc{discoveria-oai-fam-242-single-fold-diophantine-representations-r1,
author = {{DiscoverIA}},
title = {Single-fold Diophantine representations (family 242)},
howpublished = {DiscoverIA registry, entry oai-fam-242-single-fold-diophantine-representations},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-242-single-fold-diophantine-representations#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 Diophantine representation of a set of integers is a polynomial equation with integer solutions. A parameter is in the set exactly when the equation has a solution in the other unknowns. It is “single-fold” when that solution is then unique. If the manuscript were correct, it would bring a result on these representations.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI only; formalization.yaml carries the note “review: status: unchecked”, and no third-party assessment is recorded. The sources read do not say what the claimed result is.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 242.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 · Single-fold-Diophantine…link only, reading not recorded
- Lean proofgithub.com · 242.mdpage read word for word
- Lean proofgithub.com · SingleFold.leanlink only, reading not recorded
Method
The openai/math repository contains one manuscript, “Single-fold Diophantine representations”. OpenAI supplies lean/docs/242.md and 1 Comparator file, lean/ComparatorChallenges/SingleFold.lean. According to history.md, no revision is reported. 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 (Mathematical logic)
- In openai/math
- family 242, section “Mathematical logic”, 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 236 of 372, by family number
- Not evaluated : Sharp singularity rates for symmetric sign matrices (family 239)
- Not evaluated : Shelah's eventual categoricity conjecture (family 240)
- Not evaluated : Rigidity of the Turing degrees (family 241)
- Not evaluated : Single-fold Diophantine representations (family 242)
- Not evaluated : Choiceless counting does not capture polynomial time (family 243)
- Contested : The Partition Principle does not imply Choice (family 244)
- Not evaluated : The β-Barendregt–Geuvers–Klop conjecture (family 245)
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