What was already known
Earlier T³ fast dynamos had only Lipschitz spatial regularity; smooth constructions were slow or fast only along subsequences of resistivity. The paper claims the first smooth random fast dynamo, under its per-κ almost-sure definition.
AI involvement
ChatGPT 5.6 Sol Ultra found the Fourier-mode construction and growth idea. Keefer Rowan rederived and simplified it, supplied the all-time formulation, wrote the final proof and reports careful hand checking. ChatGPT later supplied a martingale lemma in response to Rowan’s prompt.
The source explicitly says the central construction and proof idea were generated essentially autonomously; later author revisions are separately credited.
Importance
The claimed smooth random fast dynamo closes a regularity gap within its per-resistivity almost-sure scope.
Limitations
The final all-time formulation incorporates Rowan’s simplification and hand check; the initial model manuscript had a different formulation.
Technical verification
Rowan explicitly reports carefully hand checking the final theorem and manuscript; this is a reported author check of the final revision, not a check reproduced here.
Human understanding
Rowan says he rederived the outline and rewrote a simpler forward-time proof using three Fourier modes.
Correction and publication history
The claimed smooth random fast dynamo closes a regularity gap within its per-resistivity almost-sure scope.
Read this published revision