Positive scalar curvature forces rational inessentiality

OpenAI

Every closed connected oriented smooth manifold of dimension at least two with positive scalar curvature is rationally inessential, without spin or fundamental-group restrictions. The aspherical obstruction also covers nonorientable manifolds through the orientation double cover.

Sources for this record

What was already known

The Gromov–Lawson aspherical obstruction and Hanke’s stronger rational-inessentiality formulation remained open in this generality; earlier methods covered narrower classes.

AI involvement AI-led

OpenAI credits its internal model with the manuscript’s parameter-manifold and shortening argument. Classical obstruction theorems remain prior human inputs.

The model-produced OpenAI-authored manuscript supplies the claimed new general argument; individual autonomy is undocumented.

Importance Major

The theorem resolves the general aspherical positive-scalar-curvature obstruction and proves a stronger rational-inessentiality statement.

Limitations

The graph-change and warped-circle shortening estimates await a documented completed expert check. A later integral scalar-curvature paper is a separate argument with related consequences.

Technical verification Reported

No completed machine or human check of the rational-inessentiality theorem is documented in the cited repository or targeted later search; Reported is the evidence default.

Human understanding Few

The manuscript describes the proof, but no named human explains its new mechanism; Few is the evidence default.

Correction and publication history

2026-10-18 · publication

If correct, the theorem resolves the general aspherical positive-scalar-curvature obstruction and proves a stronger rational-inessentiality statement.

Read this published revision