OpenAI reports unbounded stable-Morse fixed-point deficits in dimension 22

For each integer m≥1, there is a simply connected closed Kähler manifold of real dimension 22 with stable Morse number 80+1968m and a Hamiltonian diffeomorphism with exactly 80+1952m fixed points, all nondegenerate with contractible orbit loops.

Sources for this record

What was already known

A companion manuscript had already constructed a nondegenerate stable-Morse counterexample. The present claim keeps the real dimension fixed while making the numerical deficit unbounded; standard rational homology fixed-point bounds are weaker than the stable Morse number here.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Notable

Shows unbounded failure of the stable-Morse bound within one fixed dimension and manifold class.

Limitations

The linked Lean note instead checks a separate three-fixed-point example on a complex quadric, where at least one fixed point is degenerate. It does not check these nondegenerate dimension-22 examples.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.

Read this published revision