I'm still somewhat at a loss: Umbran says the framing is not relevant to an adventure being linear, but then I'm left with nothing but the text, which is inevitably linear (it begins at page 1, and finishes at page <whatever>).
The framing does not matter, in the sense that, given a path, what motivates you to get to the path doesn't change the path itself. Whether you get on the water slide because you have been shamed into it by your little brother, or to escape from a loan shark's goons - the water slide goes down, regardless.
Adventures have a shape, a
topology. It can be a line. It can be a branching tree. It can be a web of multiply connected nodes, and so on. This topology
does not have to be physical. An adventure (say, a mystery) can take place all in a single room, but the topology is of
information. Clue A -> Clue B -> Clue C -> Proof D.
Reference is made to places/rooms being able to be visited only in order. I live in a house where that is largely true, but that doesn't mean every day of my life in my house is the same!
With respect, if your daily home life resembled a D&D adventure, I don't think you'd have time to write so copiously. I am not sure your daily life is a suitable analogy.
Because different things happen, occasionally different people are in one or the other room, etc.
This is why I say that the geography
ISN'T the focus. The adventure isn't just a set of locations. If you have a linear adventure in which the PCs go through five linear rooms, and kill a dragon in the sixth, if they go to that location the next day, the dragon's going to be dead. So, clearly the next day isn't the same adventure, even if it is the same location.
It seemed to me that two different groups could play the little 6 room dungeon and have different experiences, depending on choices made, whether or not they have a Halfling who sneaks ahead, etc.
Yep. If you use a linear adventure with a group of all fighters, the resulting narrative will be different from doing it with all bards.
This is part of why linear adventures are just fine for many folks - they are interested in a lot of the small events and interactions, and may not care if the big picture isn't something they can change.
So it might be the case that we could keep "the adventure" largely intact but change the instructions, and now it wouldn't be linear anymore.
Sure. And, if you are given a dungeon with five rooms connected in a line, you can
add rooms, connect them differently, and they aren't in a line any more. Or, you can take an adventure that isn't linear, and crop stuff out, and make it linear. That GMs can edit and revise things isn't exactly a revelation.
This brings me back to the "cannot". Who imposes the cannot?
It seems like the cannot is what entails the linearity, rather than vice versa. But where does this "cannot" come from?
Yeah, this reads a lot like you are trying to lead us to a kind of gotcha conclusion. I'll note that there's a couple of things that impose linearity - one is, as you might surmise, the GM.
The other is practical reality. Linear adventures are serviceable for many, and simple to run. The time and effort to create or edit a non-linear adventure may simply not be available.
As an example, we can consider, say, 3E, and imagine a middling-high level adventure. What is provided is linear, and is constructed to provide the desired rise and fall of tension, and part of that tension is
tactical combat challenges.
But, in a 3E adventuring day, order can matter a great deal - meeting the BBEG early and late in the adventure can be different tactical challenges, and rewriting high-level tactical challenges in 3E is
NOT EASY. Many folks can't do that on the fly and expect to get similarly favorable results.
I doubt anyone in this thread could define it in a way that "Viktor T. Hothe" (a guy who posts some very good physics posts of this sort on Quora) would not spit at (well, actually he would politely correct you, but...).
Just so you know, I'm a physicist. Doubts should be interrogated, not relied upon.