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An AI-discovered smooth random fast dynamo on T³

Keefer Rowan

For the explicit iid block-refreshed smooth divergence-free velocity field U on T³ and the specified divergence-free initial magnetic mode, Theorem 1.1 gives, for each κ in [0, log(π/e)/(4π²)], an almost surely finite κ-dependent L^κ with ||B_t^κ||₂≥(L^κ)^−1 e^(t/2) for all t≥0 and a uniform positive moment bound on L^κ. Null sets can depend on κ; no single deterministic field working simultaneously for every κ is proved.

Sources for this record

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 AI-autonomous

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 Notable

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 Formal (human)

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 Full

Rowan says he rederived the outline and rewrote a simpler forward-time proof using three Fourier modes.

Correction and publication history

2026-10-18 · publication

The claimed smooth random fast dynamo closes a regularity gap within its per-resistivity almost-sure scope.

Read this published revision