Absent this, one of three conditions exist;

1. There is no monopoly. In which case violence is widespread, and there is no state.

2. There is no legitimacy. In which case violence is capricious. This is your condition of tyranny (unaccountable power).

3. Some non-state power or agent assumes the monopoly on legitimate violence. In which case it becomes, by definition the State.

The state's claim is to legitimacy. A capricious exercise would be an abrogation of legitimacy

Weber, Max (1978). Roth, Guenther; Wittich, Claus (eds.). Economy and Society. Berkeley: U. California P. p. 54.

https://archive.org/details/economysociety00webe/page/54/mod...

There's an excellent explanation of the common misunderstanding in this episode of the Talking Politics podcast: https://play.acast.com/s/history-of-ideas/weberonleadership

The misleading and abbreviated form that's frequently found online seems to have originated with Rothbard, and was further popularised by Nozick.

Of course. Glad it was cogent enough to be useful.