So what you describe in your hypothetical is a type of play in which the players main function is to declare actions that oblige the GM to reveal bits of their notes (or, if their notes run out, to make up stuff based on "logical" extrapolation from what's in their notes).I don't think that can be true. The room with stuff in it sure, but the character looking for spellbooks and not doing handstands, or brewing potions or whatever else they opt to do is entirely down to the player. We can probably map out the time searching a room takes, and point to the 5 minutes of time in that room and clearly point out which things were down to one player's choices, and which were down to the GM.
You could have (an admittedly very boring) game session that was nothing but a massive library keep, devoid of anything but romance novels, that a character wanders through looking for spell books, evaluating room by room. I'm pretty sure that could be handled much more easily/efficiently by noting the time that would take and moving on, but it certainly would still happen, and be different than if the player had decided to stop after the first room. If for no other reason than after that's done, I'd start describing the scene outside with a different time of day.
You're adding some kind of relevance criteria here to "things happening" that I don't entirely understand enough to define yet.
In your example, the notes and the extrapolation all concern the contents of the library. (The notes might tell us, say, how many volumes are in each room and what their topics are. The extrapolation is likely to be required if the players declares that they pull a volume from the middle of the third row from the door and start reading it.)
In the real world, this sort of play is very common but doesn't normally involve library books. Normally it involves the players speaking to NPCs and searching the occasional room for a <bit of paper, book, magic item, whatever>.
If we put to one side the complications introduced by the need for extrapolation due to the incompleteness of the notes, then we could say that the entire play space is defined: it is some path or other through the GM's pre-authored material. (My maths isn't strong enough to know whether there is literally a function that can define all these paths, or whether I am confined to describing it more metaphorically: still, I believe my point is clear enough.)
That is why I call it a railroad, and say that everything that happens is decided by the GM.
EDIT: I mean, suppose that I decide to have my PC do handstands or brew a potion or whatever. There seem to me to be three possibilities:
(1) That stuff has no meaningful affect on play, and after a few minutes of me describing my PC's hijinks we return to the real focus of play.
(2) The GM incorporates that action into their established fiction and logically extrapolates: my handstands knock some books from the shelf, or the fire from brewing potions sets fire to some books. We're still within the play space defined by the GM's pre-authored fiction.
(3) The GM introduces some new fiction that speaks to the concerns I have evinced via my action declarations, and play starts to be about that. Now we no longer have a railroad: we have broken out of the play space defined by the GM's notes + extrapolation therefrom, and have the sort of play that I am interested in.