Sorry, I literally have almost no time in last days, so only short answer.
@Antvasima
About dimensional structure of the Xeeleeverse.
As sufficient explain:
This is basically a Hilbert Space, that in Quantum mechanics is used to describe possible states of the system. The number of dimensions in it is correlated to the number of elements/particles in the system, and with infinity many particles in said system this number becomes infinite ( uncountably infinite infact ).
He is one of the most knowledgeable SB users in physics and mathematics(and best in Xeeleeverse), and Baxter is physicist and mathematician too, but if you want I can ask him for more detailed and scientific explanation later.
I`m, unlike sufficient, doesn't have good knowledge in the QM, but i`ll try to explain his logic. Quote stated:
If the universe has three particles,' said Reth, 'you need three numbers. Three relative distances ― the separation of the particles, one from the other - determine the cosmos's shape. And so the dust grains, mapping possible configurations, would fill up three-dimensional space -though there is still a unique grain, representing the special instant where all the particles are joined. And with four particles -' 'There would be six separation distances,' Hama said. 'And you would need a six-dimensional space to map the possible configurations.
So, we can calculate how complex is Xeeleeverse multiverses via calculating number of particles in the previous level system(if universe have 3 particles- CS would be 3 dimensional space, if we have 4 particles ― CS would be 6 dimensional space, and if we have infinite number of particles in system, we need in infinite dimensional hyperstructure).
We are know that the new Xeelee-created multiverses(yes, Baxter dislike term multiverse and never using it, he called it universes, but it is by definition multiverses, because they have infinite number of Hubble volumes(type I mv by Tegmark) , constantly branching(type III mv by Tegmark), and have higher realms, like SuSy space, CS(infinite dimensional), etc) are infinite in size and have uncountable infinite of matter, so its Config Space does have uncountable infinite number of dimensions.
Yep, Baxter in the Xeelee Sequence adding many high-end stuff, and trying to explain it, using modern-day theoretical physics, infinite dimensional Hilbert spaces as example of this.
And the most amazing in this multiverse-creating facts to me that:
1) This multiverses(or Hyperverses) was created by Xeelee in the wartime with equal(or superior) enemy.
2) Showed multiverse was created for the one insignificant species, that exist only (infinite, for Xeelee)short time in the one galaxy(Silver Ghosts), in the one universe in the one configuration of CS.
3) Multiverse creation was called standard Xeelee tactic. They are really want to create many such Hyperverses for the most of sentient species(except bad guys like Xeeleeverse humans and Qax, but later they give chance even to humans, only by different way). And this was doing in literally… zero-time, because CtC and Anti-Xeelee.
We can combine this three factors for understand how ease for the Xeelee-civilization making this projects.
Even Transcendence, godlike posthuman society that can edit CS by force of will on the level that far beyond any previously iteration of humanity, that living in their own created abstract meta-reality are still nothing to Xeelee, even members of Transcendence suggest this. sufficient suggests that even post-singularity Transcendence are still be less powerful than Xeelee(and in short story seer and silverman Silver Ghost speculated that post-ascended Transcendence can joins to the Xeelee, so perhaps it is the lowest level for the TrueXeelee members). I can say even more, they even cannot touch Xeelee. they carry over humanity, and know about future Scourge, but then understand that they are cannot help humans in any way, even their plan to ascend into pan-infinite, near-omnipotent being can give help them only chance to survive in Xeeleeverse, not defeat Xeelee, they are would be still superior to them. Also, Transcendence, with all their higher-dimensional manipulations and infinite computational abilities cannot even understand not only nature of Xeelee-civilization(they cannot comprehend them), but even how Xeelee-tech works, they are not understand scales of the War in Heavens, its still beyond them.
Actually we are don't know anything about upper limits of TrueXeelee civilization, because we are even don't see them, only their tools, . We can only extrapolating, summarizing bits of material, like hyperverse-creation, absolute superiority to the Transcendence, and actions on level beyond their level, abilities even Nightfighters manipulate CS on high level, and such. Unfortunately, we have not books from Xeelee point of view, all books written from the humans point of view, and about Xeelee interactions with humanity(and other younger races) sufficient wrote:
"A neutron star thrown by some humans on the Ring ? Send a single Nightfighter. Some humans playing with the Configuration Space ? Send a single Nightfighter. Someone tinkers with yours quantum communication system ? Send a single Nightfighter. Ghosts, humans and various other species have sent ships to investigate a quagma ark ? Send a single Nightfighter. Ect."
Some another evidence about Xeeleeverse feats:
https://forums.spacebattles.com/threads/xeelee-verse-vs-digimon-verse.395277/#post-22648036
Also, I think add Probability Manipulation to the Xeelee feats, and Mathematic manipulation or so, even teleporters in the Xeeleeverse manipulating probability on the basic level, and Xeelee Nightfighter can warp up itself into existence only because someone stated it, it was happen in the logic pool, mathematical universe, that humans creates on the beginning of their space colonization history, from Starfall:
The logic pool, he said, was a metamathematical universe. While not infinite it comprised more mathematical understanding, far more, than had yet been explored by mankind ― and in principle, somewhere within the metamathematical branching of the pool, any algorithm possible might exist. Shira said softly,
'All our science is based on the search for simple rules underlying complex phenomena. Simple algorithms can be shown to generate complexities, from the turbulent flow in a glass of water to the spiral structure of the Galaxy itself.'
'You see the idea,' Flood said. 'There's a lot of nonsense in there, but also a lot of treasure to be dug out. It's as if you have a tank full of every possible combination of words in Earthish. Most of it is dross. But in there are the finest fruits of human scientific understanding ― even those not discovered yet. But Shira has always been more ambitious than that, haven't you, Empress?'
And Nightfighter grown itself in the center of Earth only because someone stated there is possible:
'But whether or not she ever achieved her goal, she is in danger of unleashing much greater threats on humanity. For some of the minds in there are not content with stasis, with waiting to be discovered. Look at this.'
He summoned up a Virtual of his own. 'We've been tracking the consequences for years. Decades. We have our spies, in the Solar System. This is a neutrino scan we made from the Freestar just hours ago.'
It took Stillich a moment to work out that he was looking at a cross section of the Earth, deep below the granite raft of Manhattan, and the imperial bunker. And down there, swimming in the mantle, was a shape, perhaps organic, perhaps artificial, a winged shape like a stingray, like a sycamore seed. 'It isn't fully formed,' Flood said grimly. 'Not fully operational. But it soon will be.' Kale asked, 'What is it?'
'In the Friends' accounts of their dark future, there are hints of a race even more threatening to mankind than the occupiers of Earth from whom they fled. A race called—' his pronunciation was uncertain, 'Chee-lee, Zee-lee. They, or their potentialities, are lurking in the logic pool. And they are trying to break out.' 'How?' Kale snapped. 'By constructing this ship, deep in the Earth? How are they doing that?'
'We have no idea,' Flood said. 'Our only concern is to stop it, before this ship bursts from the Earth like a bird from its egg. This is a threat so potent it is trying to strike at us out of nothing more than of a statement of the logical possibility of its own existence.
Also, I think it is interesting too about Anti-Xeelee, device of Xeelee civilization:
Thanks to the logic pool Xeelee has showed up, that they only need a logical possibility of their existence, to come to be. I would even go little further and say that they can perform such a feat without the usage of the logic pool.
The situation showed to us in the Starfall is, in my opinion, very similar to how the AntiXeelee "was" created. In one of the branches in the configuration space there was a possibility that it came to be, and out of this possibility the AntiXeelee started to exist. By its own existence ( thank to it negative vector in time ) it has ensured, by taking care of the Xeelee projects, that it will be possible for it to be, in the first place. Given that it is based on quantum wave functions, the moment it will "start" to be, it will spread out through all possible configurations in the CS, or if we go with the "timeless" approach, it would be simply always present in all branches of the CS.
This is caused by the fact that quantum wave functions describe all possible histories of an object, that do exist simultaneously, at least in the abstract mathematical phase space. This is true in all interpretations of the quantum mechanics, and differences between this interpretations refer to just what does this exactly mean in a physical world.
And the logic pool, with its "I can exist simply because there was a possibility that something makes a logical statement that I can be" ads to this interpretation of the AntiXeelee additional evidence.
All credits goes to sufficient.