What was already known
Defocusing energy conservation does not control the supercritical regularity needed for continuation. The manuscript addresses the possibility of stable blowup from high-regularity data and a related Gaussian global-existence question.
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
Gives stable finite-time blowup in a defocusing energy-supercritical nonlinear Schrödinger equation.
Limitations
The pinned Lean quantifier selects an odd power above each prescribed lower bound; it does not prove the assertion for every sufficiently large odd power. The Gaussian-data consequence is separately formalized but outside this selected claim.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves stable self-similar blowup from a nonempty open Hᵏ data set for arbitrarily large odd powers on the twelve-dimensional torus.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For arbitrarily large odd nonlinear powers, some Sobolev index k>8 admits a nonempty open set of Hᵏ initial data on the twelve-dimensional torus whose defocusing nonlinear Schrödinger solutions undergo classical finite-time self-similar blowup.
- 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