Spaces larger than this do exist, obviously, but "space" is itself a nebulous notion with no formal meaning in mathematics, and the closest thing to a definition that you can find is "A set endowed with some additional rules dictating how its elements behave and interact with one another," so I don't think that's a particularly concerning factor, especially when a "spacetime" is an actual object with defined properties that do indicate an upper bound in its size.
There is no authority for definitions in mathematics, so it's no surprise that you don't find a clear definition of such a general concept. That said, anything that has established itself to be called space has done so because many authors thought it has space-like properties.
in any case, just like there is no authority on definitions in mathematics there is also no authority for what "spacetime" means. Spacetime is defined as any model unifying space and time. Your assumption of separability isn't something necessarily included. It's a stance one can take, but not a stance on has to take. And that is an important distinction.
If you go around and tell works of fiction that their spacetime consisting of aleph_45 spatial dimensions and one time dimension is not actually spacetime because it isn't separable, then you're invoking authority you don't have.
It's one thing to say "we as a community decided that spacetime goes up to 1-A and as such we rank characters transcending it as such" and another to make rules that assume that no fiction can have spacetime above that level.
That's a fair enough point, but we aren't actually telling fiction how to behave, are we? Indexing as a whole is built while having in mind the basic assumption that some underlying principles are at play, whether those be physical or purely mathematical; if fiction decides to go against them, then that's fine, but if it doesn't outwardly break them at any point, I don't see why we wouldn't consider them applicable, especially since the vast majority of the 1-A characters on the wiki are already depicted as being aspatial and atemporal, anyway.
There is a huge difference between saying "physics works" and "spacetime goes only so high due to some mathematical consideration no author ever actually did". The former everyone writing fiction would probably agree with unless their work explicitly plays otherwise. The latter? Not so much.
If you aren't telling fiction how to play, then characters that haven't demonstrated being beyond time and able to move backwards through it wouldn't be assumed to do so. Otherwise, you are inventing abilities for them the work itself doesn't do. There is a difference between evaluating things we are shown and applying deduction to arrive at abilities we are not shown.
It's like saying "The character has city level punches. According to physics city level, punches should cause nuclear fusion. Therefore this character's punches can cause nuclear fusion." Nothing wrong with that as far as physics goes, but unless they actually show doing that we will not assume they can do it, since that would be inventing new abilities.
Most 1-A's are atemporal? Good, but why should that mean the rest should be it as well?
And, to get back to the point why we were having this debate, why should we say characters above spacetime are faster than those of Immeasurable speed in a larger spacetime? If we acknowledge that these fictions are allowed to have their own systems, then we can't insist on transcending spacetime in one cosmology being always faster than what characters that don't do it have.
So either one must make it so that Immeasurable speed can be faster than Irrelevant speed or one has to alter the definition of Irrelevant, so that characters that are faster than baseline spacetime transcending irrelevant ones are Irrelevant as well, even if they are not above spacetime in their verse at all.
The latter is what I'm trying to do when I say we should define Irrelevant as transcending (being of irrelevant speed) in at least so-and-so many dimensions of time.
I also don't exactly understand what you mean by "the outgrowing of spacetime would be due to getting too large for space, not time," since time-like directions are themselves not that different from spatial dimensions, geometrically-speaking, and only differ in terms of their causal signatures and eigenvalues being negative (Instead of being positive, such as with spatial dimensions)
If characters get "bigger" than we are talking about their extension in space expanding, not their extension in time. That's because dimensions are independent of each other.
So if you get too big to be contained in spacetime, that doesn't mean you now extend through all of time or that you can freely move backwards against its flow.
For example: In mathematical terms, you can have an object that has finite, but greater 0, expansion in aleph_45 dimensions (some of these spatial, some maybe not) and 0 expansion in the 1 dimension which we defined to represent good old normal time. However, like usual things it still has a position in time. That could be 0 for example. According to you this object would transcend spacetime due to being too large. However, being beyond spacetime in this fashion doesn't give it expansion in the time dimensions. Neither can we conclude that if this object can move backwards in time. It could still be bound by the rules that if it changes its position it may only do so in the forwards direction of the time axis.
Our combat speed includes the capability to react to attacks on your speed level or less. So if this existence had immeasurable or greater combat speed it would need to be able to react to an attack backwards in time. However, despite being large this being has no reason for being able to block an attack on its prior state.
In conclusion: It doesn't suffice to transcend spacetime (in your definition of spacetime) by size to be Immeasurable or higher fast. One has to transcend spacetime in a particular fashion. That can be that one can move through them, is omnipresent through them or by all time as happening at once out of onces perspective, but size or power alone don't suffice.
I expect most 1-A characters to have no problem with that criteria, but it is one we should require none the less.
I wouldn't really say that, frankly, considering that the size of a Proper Class (When actually formalized, that is) is practically just equivalent to the smallest cardinal that is too large to be actually constructed from within your model of the Universe of Sets, and so their precise scale varies depending on the Axioms which you endow your theory with. Ord is effectively just ω when defined over a framework that excludes the Axiom of Infinity, for instance.
It is a huge change, because you just lose lots of very basic mathematical concepts in the process. Even more talking about proper classes. You can't even put those together into a proper container.
If you think that at that point any character can actually proof being anything like that outside of literal direct statement or lots of subjective handwaving you would be wrong. At that point, you're just talking what to call a level where the thing you name it after has no actual relevance to its classification. It just some next level of transcendence.
And with that I have written enough for the day. Other replies not soon.
