Physical rigidity conjecture for generalised Frenkel–Gross connections

A generalised Frenkel–Gross $G$-connection is a connection on the multiplicative group with an irregular singularity at infinity of slope $1/h$ and a regular singularity at $0$. The original Frenkel–Gross connection is the case with unipotent monodromy. Physical rigidity conjecture. Generalised Frenkel–Gross connections are physically rigid. This is a de Rham analogue of a conjecture of Heinloth, Ngo, and Yun. The source has established cohomological rigidity and regular monodromy, but does not provide a resolution of physical rigidity in the supplied text.