PreprintCC BY 4.0arXiv
Fold Catastrophes in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog
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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BibTeX
@misc{niemi2026fold,
title = {{Fold Catastrophes in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog}},
author = {Antti J. Niemi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24490},
eprint = {2609.24490},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24490},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fold Catastrophes in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog
AU - Antti J. Niemi
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.24490
UR - https://arxiv.org/abs/2609.24490
AB - 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 A_2 fold. A subsequent three-to-five transition precedes a burst-like regime of recurrent fold catastrophes and near-caustic activity.
ER -