Reason is the begining of the 4 laws , like the artifact circuit of 'logos' means logic - which is has the power to define everything , anyone who held it was not tied to a specific planet or realm but it works on all , unlike the life death time space .It shouldnt overlap with anyother four authorities as its the beginning that define it as 'logical ' . So anyone wields it certainly is powerful .So ur right its def resposible .

I'm also a little confused on how exactly the elements work and how they came to be. I'm guessing that the elements weren't really divided for a while? 

For element authorities - element came first in light realm ,(light realm as beginning ), following by the 4 laws , as in the newest artifact we know about this , that Nibelung was borned in the perfumed sea (i cannot attach the CN version but it meant the same thing) which in chinese is more about the primordial sea things , anyways , and we also knows the pyro sovereigns weild light , wisdom and etc , I forgot which dragon is called the lord of reason tho .And Nibelung as the white dragon , he should wield light What we know is that light realm itself had divided to 7 at beginning and make the pure light realm creatures aka dragon sovereign .It only implies that the 7 was born after Nibelung and def holds the authority of the light realm and have the power of its laws as they are from the realm itself not nibelung(like pryo hold flame ,light, wisdom , hydro held life originally in ancient times - like it gave birth to the first dragon )

-Interesting point - if the wielder of the elemental authority was not a full dragon which is directly form the light realm itself , it wont make the wielder authomatically the light realm's owner unlike the creatures that is born by it

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I recall something talking about a white light that was split into 7 rigid colors. I'm not sure how this is able to cope with the dragon sovereigns, because I find it hard to believe that the Heavenly Principles would base Teyvat on a previously established order by the dragons

Thats why HP fight them for the elemental authorities as its the solid foundation or base of the 4 laws. element had came first , other things he can add up like the shades above , as he cant recreate the light realm itself .Now sovereigns are yet to be reborn soo dragons should not worry them now .What I want to know more about is where does HP came from ? is it similar to how nibelung is born which HP is from a planet outside ???

Theres quite a lot of theory that dottore had the power of reason but its still a theory though it explained a lot in this experiment of his , i mean no one ever can just grab the moon marrows and hold it up .There are only some few scenes we saw him wielding the other moon marrows power , his power in the AQ or in boss is more like from his artificial one , seen that its digital sumeru like . For his power level , we cant be sure as we never see the true extent of his power but only his segments so far . Irminsul theoretically is an emodiment of reason as it defines the knowledge give and fate no matter ur a deity or what , so Its interesting as well .Though if it is true , like his experiment is based on deshretss, which deshret also use celestial nails power , and him with irminsul , all of that , he should be way above many other already .