Complete model spaces do not force Lie-group regularity

The problem asks whether every infinite-dimensional Lie group modelled on a complete locally convex space is regular. The reported construction gives a negative answer to this question and to the related Glöckner–Neeb question about automatic multiplication growth.

July 2026 counterexample

The preprint constructs a contractible complex analytic BCH–Lie group $H$, modelled on the complete Silva space $\varphi_{\mathbb{C}}$, with homeomorphic exponential map $\exp_H:L(H)\to H$, yet $H$ is not even $C^0$-semiregular. It exhibits smooth curves $\gamma_\lambda$ converging to zero in $C^\infty([0,1],W)$ for a finite-dimensional $W$, while $U'(t)=\gamma_\lambda(t)U(t)$, $U(0)=1$, has no $H$-valued $C^1$ solution on $[0,1]$. The associated groups are claimed not to be $C^k$-semiregular for any $k\in\mathbb{N}_0\cup\{\infty\}$.

Current status (as of July 2026): The universal regularity assertion is claimed false by an explicit complete-space counterexample, but independent verification and publication status remain open.