There is not a scientific proof YET, but i think it can be done: for that we would need to program the “corner-stone”, which would be the *nix-program #1 - something that could show practically what the pioneers of the *nix system envisioned. This practical proof is possible, if we deep dive into the POSIX definition to analyze for what it was made.
unix is a trademark, but what counts is the architectural vision behind it (D. Richie&co.) I think it would be better to avoid the tradmarked word (sry for using it) - *nix may be a proper word (although it implies that it is a whole group)