Gilbert-Pollak conjecture on the Steiner ratio:Consider a set $P$ of $n$ points on the euclidean plane. A shortest network interconnecting $P$ must be a tree, which is called aSteiner minimum treeand denoted by $SMT(P)$. A $SMT(P)$ may contain vertices not in $P$. Such vertices are calledSteiner points, while vertices in $P$ are calledregular points. A spanning tree on $P$ is just a tree with vertex set $P$. A shortest spanning tree on $P$ is also called aminimum spanning treeon $P$, denoted by $MST(P)$. TheSteiner ratiois defined to be $$\rho=\inf\{L_s(P)/L_m(P)|P\},$$ where $L_s(P)$ and $L_m(P)$ are lengths of $SMT(P)$ and $MST(P)$, respectively. Gilbert and Pollak conjectured that $p = \sqrt{3}/2$.

I find recently that the proof of the Gilbert-Pollak conjecture given by D. Z. Du and F. K. Hwang in 1990 is disproved by N. Innami etc. (The Steiner Ratio Conjecture of Gilbert-Pollak May Still Be Open and The Steiner Ratio Gilbert–Pollak Conjecture Is Still Open). When I check related comments about this case on the Internet, I find there seems to be few people that care about this (very few information).

Is this conjecture still open? Is there anyone trying to sovle this problem in other ways or to fix the proof of D. Z. Du and F. K. Hwang?