I stand by them. Though, as always, quotes and WoBs at signings aren't always as deliberately thought out as I'd like them to be. Answering questions on the fly can be challenging, and my phrasing can be bad in retrospect.
But no shard was in residence on First of the Sun during the events of that story. The investiture on that planet is residue, normal investiture from Adonalsium. Everything happening there could happen with or without a shard present. Indeed, I would say that no shard was ever "in residence" on First of the Sun.
The being called Patji still exists, and is a shard of Adonalsium. Shards in the past have been interested in First of the Sun, and have meddled in small ways there. (Like they have on a lot of shardworlds.)
Note that I might have been a little misleading in the first quote by bringing up Threnody, which is a real corner case in the cosmere because of uncommon events there.
That said, I'm sure that every story I write about a planet will bring up the quirks and unusual interactions of the magic there, because that's kind of what I do. (First of the Sun has its own oddities, as mentioned in Arcanum Unbounded.) Every planet is likely to end up as a corner case in some way, just like every person is distinctive in their own way, and never fully fits expectations.
I still consider one of the major dividing lines between "major" and "minor" shardworlds (other than Shard residence) to be in strength of access to the magic, and control over it. I intend the minor shard worlds to involve interactions with the magic as setting--coming back to spren, you could have a minor shardworld with people who use, befriend, even bond spren. (Or the local equivalent--Seon, Aviar, etc.) But you'd never see power on the level of the city of Elantris, the actions of a Bondsmith, or even the broad power suite of a mistborn.
But, as ever, the cosmere is a work in progress. The needs of telling a great story trump things I've said about what I'm planning. (I do try as much as I can to avoid having two texts contradict one another. And when they do, that's often a lapse on my part.)
So the Investiture on First of the Sun is associated with a Shard or is it residue, normal investiture from Adonalsium?
Cause the question was a follow up (on this) where you revealed that all Investiture in Cosmere got assigned to a Shard even if it wasn't part of a Shard.
And then you said that the one on First of the Sun is directly associated with one of the Shards (and since later you revealed Patji to be an avatar of Autonomy (also, what are avatars and how do they work?)) we took it to mean that at one point Autonomy Invested in First of the Sun.
But now you're saying it didn't?
If there was no Shard ever on First of the Sun but Patji is a Shard/avatar of a Shard then where is Patji, actually?
Could you please clarify all that?
So the Investiture on First of the Sun is associated with a Shard or is it residue, normal investiture from Adonalsium?"
The reason I have so much trouble answering these questions (and you'll see me struggling to get an answer in the 10-15 seconds I have when someone asks me in a signing line) is because this isn't an either or. Is this computer I'm using matter associated with Earth, the Big Bang, or such-and-such star that went supernova long ago? Well, it's probably all three.
When people ask, "What shard is this investiture associated with" it gets very complicated. Shards influence and tweak certain investiture, giving it a kind of spin or magnetism, but all investiture ever predates the shattering--and in the cosmere matter, energy, and investiture are one thing.
I always imagine investiture having certain states, certain magnetisms if you will, associated with certain aspects of Adonalsium. So it's all "assigned" to a shard--because it's always been associated with that Shard. To investiture, Adonalsium's shattering meant everything and nothing at the same time.
We generally mean the term "Invested" to mean a Shard has taken permanent residence in a location, a kind of base of operations--but at the same time, this is meaningless, since distance has no meaning on the Spiritual Realm, where most Shards are. So imprisonment of a Shard like Ruin or Odium is a crude expression--but the best we have.
Autonomy never "invested" on First of the Sun. But even answering (as someone else asked) if they created an avatar without visiting is a difficult thing to explain--because even explaining how a shard travels (when motion is irrelevant) is difficult to manage. It's a subject that I intend to be up for debate, discussion, and argument by in-world philosophers and arcanists.
You can see why I have such troubles explaining these things at signings--and why I fail when I try to, considering the time limitations and (often) fatigue limitations placed upon me. These are concepts I intend to spend entire, lengthy epic volumes explaining and exploring.
Let's say you were Autonomy, and you have--through expanding and exploring your understanding--found a gathering of investiture that has always been there, you always knew about, but still didn't actually recognize until the moment you considered and explored it. (Because even though your power is infinite, accessing and using that infinity is beyond your reach.) Were you "invested" there? No, no more than you're invested on Roshar, where parts of what were Adonalsium still exist that are associated with you (in the very fabric of mater and existence.) But suddenly, you have a chance to tweak, influence, and do things that were always possible, but which you never could do because you knew, but didn't know, at the same time.
And...I'm already into WAY more than I want to be typing this out right now. If it's confusing, it's because it's practically impossible for me to explain these things in a short span of time.
I'm going to leave it here, understanding that no, I haven't fully explained your question. (I didn't even get into what avatars are, what Patji was, and what happened to Patji the being--and how that relates to Patji the island.) But hopefully this kind of starts to point the right direction, though I probably should have just left this question alone because I bet this post is going to raise more questions than it answers...