What was already known
Córdoba and Martínez-Zoroa developed the forced-blowup program and had blowup with rougher forcing; Córdoba, Martínez-Zoroa and Zheng had an unforced solution with lower regularity at a point. Smooth-forcing Euler blowup within this construction was the new step, distinct from the later OpenAI unforced Euler claim.
AI involvement
Buckmaster credits Córdoba and Martínez-Zoroa with the earlier program. An LLM generated the new proof under Alpöge and Buckmaster’s direction; Claude wrote the Lean code under Alpöge’s direction.
The new proof was LLM-generated within a human-directed program; its historical starting idea belongs to Córdoba and Martínez-Zoroa.
Importance
Achieves finite-time Euler blowup with forcing smooth through the blowup time.
Limitations
The result uses external forcing and does not settle unforced Euler blowup. The reported Lean theorem covers the forced blowup and uniqueness claim, but not every geometric detail in the later manuscript. No complete human proof review is documented.
Technical verification
The source reports a complete Lean 4 proof of the matched forced-Euler blowup proposition, including vorticity divergence and the stated uniqueness class. Alpöge checked statement alignment, but no completed human proof check is documented. The more specific torus support and initial-swirl details of the later manuscript are outside the cited Lean proposition.
Formal checking
The source reports a complete Lean 4 proof of the matched forced-Euler blowup proposition, including vorticity divergence and the stated uniqueness class. Alpöge checked statement alignment, but no completed human proof check is documented. The more specific torus support and initial-swirl details of the later manuscript are outside the cited Lean proposition.
- Checker
- Lean 4 kernel and Comparator, as reported by Alpöge and Buckmaster's release
- Scope
- Existence of smooth-forced finite-time Euler vorticity blowup on R3 with finite energy, divergent vorticity integral and preterminal uniqueness
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the inherited layered-vortex program and the manuscript's construction, but Buckmaster expressly described the new model proof as still being understood and rewritten. The later manuscript does not establish that this gap was fully closed.
Correction and publication history
An LLM generated the new proof under human direction; the matched core theorem was checked in Lean.
Read this published revision