Not evaluated
Counterexamples to strong forms of Arnold's fixed-point conjecture (family 347)
The gist
On October 6, 2026, OpenAI published five manuscripts on Hamiltonian fixed points, from an unreleased internal model, claiming, among other results, counterexamples to Arnold bounds.
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-347-counterexamples-strong-forms-arnolds-fixed-r1
@misc{discoveria-oai-fam-347-counterexamples-strong-forms-arnolds-fixed-r1,
author = {{DiscoverIA}},
title = {Counterexamples to strong forms of Arnold's fixed-point conjecture (family 347)},
howpublished = {DiscoverIA registry, entry oai-fam-347-counterexamples-strong-forms-arnolds-fixed},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-347-counterexamples-strong-forms-arnolds-fixed#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
These manuscripts belong to differential geometry. If their results were correct, some would describe Hamiltonian fixed points fewer in number than the stable Morse number. One is set in dimension twenty-two, another on the “symplectic quadric threefold”.
What remains unclear
The sources read do not state the results of the five manuscripts. The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI and has not been verified by a third party: the repository records it as “review: status: unchecked”. A single Comparator statement accompanies the five manuscripts, and the sources read report no third-party assessment.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 347.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 · …in-Dimension-Twenty-Two…link only, reading not recorded
- Repositorygithub.com · Sharpness-of-the-Cyclic…link only, reading not recorded
- Repositorygithub.com · …October-5-2026link only, reading not recorded
- Repositorygithub.com · A-nondegenerate…link only, reading not recorded
- Repositorygithub.com · A-degenerate…link only, reading not recorded
- Lean proofgithub.com · 347.mdpage read word for word
- Lean proofgithub.com · ArnoldCounterexample.leanlink only, reading not recorded
Method
Five manuscripts of family 347 are listed in CONTENTS.md of the openai/math repository. Three are dated October 5, 2026. The first is “Hamiltonian Fixed Points Below the Stable Morse Number”. The second is “Hamiltonian Fixed Points Below the Stable Morse Number in Dimension Twenty-Two”. The third is “Sharpness of the Cyclic Integral Floer Bound Below the Stable Morse Number”. Two are dated September 23, 2026: “A nondegenerate counterexample to the Morse-number Arnold bound” and “Three fixed points on the symplectic quadric threefold”. The folder of the latter is named A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026. The Lean comprises lean/docs/347.md, which “describes the scope of the Lean formalization”, and one Comparator statement: lean/ComparatorChallenges/ArnoldCounterexample.lean. The family is present in the `sources` of formalization.yaml. 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).
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 347, section “Differential geometry”, 5 manuscripts dated Sep 23, 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
- 8 : 1 read word for word, 7 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 341 of 372, by family number
- Not evaluated : The metric Blaschke conjecture (family 344)
- Not evaluated : Infinitely many closed geodesics on spheres and three-manifolds (family 345)
- Not evaluated : Sharp singular-set bounds for stationary integral varifolds (family 346)
- Not evaluated : Counterexamples to strong forms of Arnold's fixed-point conjecture (family 347)
- Not evaluated : Nonnegatively curved Einstein four-manifolds and a topological gap (family 348)
- Not evaluated : The Solomon–Yau least-volume conjecture (family 349)
- Not evaluated : Yau's nodal conjecture: surfaces and counterexamples (family 350)
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