I was thinking more along the lines of governmental continuity, which has just as arbitrary lines. But less arbitrary in some cases like conquest or dynastic change. Like there was something that happened between Julius Caesar and Agustus. The line isn't super clear, but the Republican government and the empire definitely have some key differences even if the Senate was never really disolved.

But I remember Louis XIV saying something like "I die, but the state remains". So I think in some proto form "the state" or something larger than just the ruler has existed on and off throughout history.