**The *p*-adic Lindemann-Weierstrass Conjecture**: Let $\alpha_{1},\ldots,\alpha_{N}\in\overline{\mathbb{Q}_{p}}$
  be $p$-adic algebraic numbers satisfying $\left|\alpha_{n}\right|_{p}<p^{-\frac{1}{p-1}}$
  (so that $\exp_{p}\left(\alpha_{n}\right)\in\mathbb{C}_{p}$) for all $n$. Then, $\exp_{p}\left(\alpha_{1}\right),\ldots,\exp_{p}\left(\alpha_{N}\right)$
  are algebraically independent over $\mathbb{Q}$.

I'm a graduate student who is considering taking on this problem for my doctoral dissertation

[This article from 2008 by M. Waldschmidt][1] says that the conjecture is still open (it lists it as conjecture 5.16).


  [1]: https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/AWSLecture5.pdf

I was wondering if that was still the case.