Fold Catastrophes in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog
Antti J. Niemi
Abstract
A two-component Bose--Einstein condensate can host a pseudospin Hopf texture coupled to the viscous normal flow of its thermal cloud. Motivated by OpenAI's reported finite-time Navier--Stokes singular solution, we evolve such a texture in a smooth flow reproducing the geometry and similarity scaling of the collapsing axisymmetric core. The evolution creates and annihilates preimage pairs while preserving the Hopf charge. The first one-to-three transition exhibits the square-root opening characteristic of a Thom A2 fold. A subsequent three-to-five transition precedes a burst-like regime of recurrent fold catastrophes and near-caustic activity.
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