Is the $S$matrix conjecture still open? I mean the one listed as Problem 7 in this survey.

To my knowledge, this problem is still open. There has been partial progress on it in the past few years, but it still seems quite far from resolved. The latest paper that I am aware of is: here, though unfortunately behind a pay wall. 


Here is a more recent paper: Roman Drnovšek, On the Smatrix conjecture. It (re) proves for the case of $n$ odd the conjecture restated here for convenience: 

