Here's the small proof as requested:
https://www.youtube.com/watch?v=W4T_JR8LAfc
Davy was raiding and had killed Jack. Jack then froze Davy and left him there. After this, Jack returned to outside his house and waited. In the video Jack tries to excuse the freeze by saying that Davy "didn't say raid". Even if Davy had broken some rule, Jack's way of dealing with it is unacceptable. Given with the fact that Davy hadn't broken any rules, this makes Jack's behaviour even worse.
If proof of more rulebreaks is required I can provide, but I hardly think it's needed. Multiple people have confirmed that Jack is unfit for mod, and this video shows just how bad he is.