In Part Two, chapter XI of Economy and Society [1], Max Weber defines the modern bureau with its paperwork included: the body of officials working in an agency, "along with the respective apparatus of material implements and the files makes up a bureau." Why are the files part of the definition?
Start with a tax letter, signed by an official you will never meet. You pay, and you would pay just the same if someone else had signed it. The authority isn't the official's. Under what Weber calls rational-legal authority (Part One, chapter III), obedience "is owed to the legally established impersonal order" and reaches the person only through the office they hold.
Now the official on your case quits mid-file. A new hire picks it up, and nothing changes for you. That works only if the case never lived in the first official's head. So the office keeps its state outside any official: its management "is based upon written documents (the 'files'), which are preserved." Weber lists the files without deriving them, but they follow from authority that sits in the office. The office outlasts every officeholder, so its record of every case has to as well.
I worked out the files myself from the clerk who quits mid-case. It's a shape I know from software: stateless workers in front of a database, where any worker can die because the state lives in the store. It's why I read Weber for multi-agent design: an agent starts every session with no memory of the last, so it turns over faster than any clerk.
References
Economy and Society [link]
Weber, M., 2013. University of California Press.