Smooth Random Fast Dynamo on the Three-Torus
Constructed an explicit class of smooth random, time-dependent incompressible velocity fields on T^3, obtained by alternating smooth shear flows with iid random phases on finite time blocks. For every fixed sufficiently small resistivity, the magnetic field has an almost-sure exponential growth rate at least 1/2, together with a time-uniform lower bound whose random prefactor has a resistivity-uniform inverse-moment estimate. This is one variant case of Arnold's 1994 fast-dynamo problem, not the problem itself: Arnold asks for a field that is smooth, autonomous and deterministic all at once, and this one keeps the smoothness while giving up the other two. The sibling entry on this site relaxes the opposite hypothesis, keeping an autonomous deterministic field at Lipschitz regularity. Neither settles Arnold's problem as posed, which remains open.
Exact FrontierDelta
Scope and record
Occurred: Oct 29, 2026
Delta type: REGISTRY REVISION
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Smooth Random Fast Dynamo on the Three-Torus · Smooth random fast dynamo
Confidence: Not scored
Registry verification: unreviewed · preprint · variant
Attribution
VibeMathed
registry · event recorded by
ChatGPT 5.6 Sol Ultra
model · ai model contributor · OpenAI
Keefer Rowan
human · human collaborator
Lineage and corrections
Corrects Smooth Random Fast Dynamo on the Three-Torus →
Supersedes Smooth Random Fast Dynamo on the Three-Torus →
Constructed an explicit class of smooth random, time-dependent incompressible velocity fields on T^3, obtained by alternating smooth shear flows with iid random phases on finite time blocks. For every fixed sufficiently small resistivity, the magnetic field has an almost-sure exponential growth rate at least 1/2, together with a time-uniform lower bound whose random prefactor has a resistivity-uniform inverse-moment estimate. This is one variant case of Arnold's 1994 fast-dynamo problem, not the problem itself: Arnold asks for a field that is smooth, autonomous and deterministic all at once, and this one keeps the smoothness while giving up the other two. The sibling entry on this site relaxes the opposite hypothesis, keeping an autonomous deterministic field at Lipschitz regularity. Neither settles Arnold's problem as posed, which remains open. parent of this event
This event attributed to ChatGPT 5.6 Sol Ultra
Smooth Random Fast Dynamo on the Three-Torus evidence for this event
Smooth Random Fast Dynamo on the Three-Torus parent of this event
VibeMathed record: Smooth Random Fast Dynamo on the Three-Torus evidence for this event
This event attributed to Keefer Rowan
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