Not evaluated
Uniform limit-cycle bounds in Hilbert's sixteenth problem (family 143)
The gist
On October 6, 2026, OpenAI announced, with an unreleased internal model, two manuscripts on limit cycles of planar polynomial systems and of quintic Liénard systems.
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-143-uniform-limit-cycle-bounds-hilberts-r1
@misc{discoveria-oai-fam-143-uniform-limit-cycle-bounds-hilberts-r1,
author = {{DiscoverIA}},
title = {Uniform limit-cycle bounds in Hilbert's sixteenth problem (family 143)},
howpublished = {DiscoverIA registry, entry oai-fam-143-uniform-limit-cycle-bounds-hilberts},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-143-uniform-limit-cycle-bounds-hilberts#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 limit cycle is a closed and isolated trajectory of a system of differential equations in the plane; a quintic system has degree five. If the manuscripts held, the first would give uniform bounds on limit cycles of planar polynomial systems. The second concerns two limit cycles for quintic Liénard systems.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, and its tracking file carries the mention “unchecked”. No third-party verification is recorded. It is not known in what sense the bounds are uniform, nor how far the Lean statement covers the manuscripts.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 143.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-bounds-for-planar…link only, reading not recorded
- Repositorygithub.com · two-limit-cycles-for…link only, reading not recorded
- Lean proofgithub.com · 143.mdpage read word for word
- Lean proofgithub.com · QuinticLienard.leanlink only, reading not recorded
Method
The openai/math repository contains two manuscripts dated September 24, 2026: “Uniform bounds for planar polynomial limit cycles” and “Two limit cycles for quintic Liénard systems”. The file lean/docs/143.md describes the scope of the Lean formalisation, with 1 Comparator statement. The family is among the sources of formalization.yaml, and 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: “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 (Dynamical systems and ergodic theory)
- In openai/math
- family 143, section “Dynamical systems and ergodic theory”, 2 manuscripts 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
- 5 : 1 read word for word, 4 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 139 of 372, by family number
- Not evaluated : Memory–sample lower bounds for noiseless Gaussian regression (family 140)
- Not evaluated : The existential theory of the reals and existential–universal sentences in the counting hierarchy (family 141)
- Not evaluated : Deterministic polynomial factorization over prime fields (family 142)
- Not evaluated : Uniform limit-cycle bounds in Hilbert's sixteenth problem (family 143)
- Not evaluated : Banach's simple Lebesgue-spectrum problem (family 144)
- Not evaluated : Rokhlin's multiple-mixing problem (family 145)
- Not evaluated : Sinai's positive-entropy conjecture for the standard map (family 146)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.