Autonomous Lipschitz Fast Dynamo on the Three-Torus
One variant case of Arnold's 1994 fast-dynamo problem, not the problem itself. Arnold asks for a single velocity field on T^3 that is smooth, divergence-free, autonomous and deterministic, fixed independently of the magnetic diffusivity, and that grows the magnetic field exponentially at every small enough diffusivity. The field constructed here is all of that except smooth: it is Lipschitz, not C^1. The sibling entry on this site relaxes the opposite hypothesis, keeping a smooth field but making it random and time-dependent. Neither settles Arnold's problem as posed, which remains open.
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Scope and record
Occurred: Aug 3, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. Editorial metadata: CC BY 4.0; linked content retains its own rights.
Canonical aliases: Autonomous Lipschitz Fast Dynamo on the Three-Torus · Lipschitz fast dynamo
Confidence: Not scored
Registry verification: unreviewed · preprint · variant
Attribution
VibeMathed
registry · event recorded by
Lukas Niebel
human · human collaborator
GPT-5.5 Pro
model · ai model contributor · OpenAI
GPT-5.6 Sol
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Lukas Niebel
This event attributed to GPT-5.5 Pro
This event attributed to GPT-5.6 Sol
VibeMathed record: Autonomous Lipschitz Fast Dynamo on the Three-Torus evidence for this event
Autonomous Lipschitz Fast Dynamo on the Three-Torus parent of this event
One variant case of Arnold's 1994 fast-dynamo problem, not the problem itself. Arnold asks for a single velocity field on T^3 that is smooth, divergence-free, autonomous and deterministic, fixed independently of the magnetic diffusivity, and that grows the magnetic field exponentially at every small enough diffusivity. The field constructed here is all of that except smooth: it is Lipschitz, not C^1. The sibling entry on this site relaxes the opposite hypothesis, keeping a smooth field but making it random and time-dependent. Neither settles Arnold's problem as posed, which remains open. parent of this event
Autonomous Lipschitz Fast Dynamo on the Three-Torus evidence for this event
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