What was already known
Earlier results covered bounded solutions, lower dimensions, restricted exponent or weight ranges, stability, decay or energy conditions. The unrestricted subcritical nonexistence statement remained conjectural.
AI involvement
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
Resolves the subcritical Hénon–Lane–Emden conjecture across the stated powers, weights and dimensions.
Limitations
The inequality is strict; the critical equality case is not included. No condition at infinity is imposed.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves the full stated nonexistence result for origin-continuous, off-origin classical solutions.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For n≥2, p,q>0 and real weights A,B satisfying (n+A)/(p+1)+(n+B)/(q+1)>n−2, the Hénon–Lane–Emden system has no strictly positive entire solution continuous at the origin and C² away from it.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
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
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision