RAW, since your "smartness" is measured by your COG score and INT score, I'd say the smartest a given cyberbrain can handle is given by the aptitude maximum for the morph it is installed in (for some reason or other, probably available headspace in most cases, the morph puts limits on how powerful a cyberbrain you can put in there.) One thing to consider is the "Promethean Fork" entry on page 171 of the Firewall book. A "pale imitation" of a Promethean, an effective delta fork for them, has COG, INT, and WIL at 40. Which is the highest any aptitude can go in the game. So not only are our cyberbrains incapable of processing a full Promethean, the Eclipse Phase ruleset can't handle it either. Of course, a funny thing about them being so smart that the rules can't handle them, they're also so smart that they can say "screw the rules I'm a god". You still wouldn't be able to give them any stats that make sense to the system, but that should be okay as long as they never do anything that would require having stats (which they shouldn't because RPGs tend to either get silly or quite boring for the PCs once a god starts throwing their weight around). As far as Stephen Hawking goes, yeah I'm sure a cyberbrain can handle him. Remember that 10 is the (modern, unmodified) human average for any aptitude. This lends itself easily to comparison to the IQ test, where 10 COG would be like scoring 100 (because the IQ test is, ideally, calibrated so that 100 is human average). So that would make COG 15 like having an IQ of 150, and COG 40 like having an IQ of 400 (though I think the comparison breaks down there, does the test even go that high?). So as you can probably see, there's some real brainiacs walking around in the world of Eclipse Phase. Which isn't too surprising when you consider that you can literally buy smarts in this setting. For twelve easy payments of 999.99Cr*, you too can unravel the secrets of the universe! *Plus shipping and handling depending on your location. Taxes and additional fees may apply. Visit our mesh node for details.

to put it into a relative comparison a fork capable of working ina cyber brain or meat brain would be in the gamma or epsilon grade for a normal transhuman, aka backwash.

iirc glory or the core book directly stated or implied that an entire titan (pre infection) could be run on a cpu block the size of a loaf of bread

Panopticon, somewhat ambiguously, says that a 100 quantum computer core can host a seed AGI, which may or may not be an ASI. I'd guess it would be enough to create the transcendent fork-tree which I think is needed to turn an AGI into an ASI. To make matters more complicated, egos aren't generally run on quantum computers, which makes comparing them harder. One of the only things I can find for ego numbers and computer volume is the Portable Server from Transhuman, which is about the size of a carry on luggage, and can hold 10 egos. The size of carry on luggage is around 43 liters external volume, so taking this literally, it should take about 4.3 liters of computation substrate to run an infomorph. We know this is wrong though, as ectos can run infomorphs, and the human brain is about a quarter of that volume. This is probably because Eclipse Phase servers (especially rugged portable ones) are described as armored and massively redundant. As an example, by RAW, the portable server could take an entire pistol of SMG magazine without any loss of functionality. That's a *ton* of redundancy, so saying that an non redundant less-error checking piece of hardware would be 100-1000 times smaller seems fairly reasonable. 4.3 liters/1000 gives a volume slightly larger than a credit card. A credit card has a volume of 3.5 cm3, so that makes a pretty good upper bound for the least an infomorph can run on. Ectos also have radio transceivers and batteries, so chopping the volume down by half seems pretty justifiable. 1.75 cm3 per human ego. Assuming that processing block had a 10 liter volume (1 meter x 15 cm x 15 cm) for a low end, 100 liters (1 meter x 1 meter x 1 meter) for mid end, and 200 liters (2 meters x 1 meter x 1 meter) that gives it an approximate power of: 5714 egos low end 57140 egos mid end and 114300 egos high end. That's a ballpark estimate of the kind of power needed to *birth* a seed AI, with ASIs presumably using much more power. (The Myrmidon TITAN fragment is from pg 21 of Glory, is people want to read that section). This would be a pretty fragile machine, for a military satellite, but it also would vastly more efficient to build a single large and extremely powerful computer than tape tens of thousands of iPhone processors together, so these numbers could easily be several times higher. I'd assume that transhuman informorphs are nowhere near as efficient as something running on dedicated hardware, which an ASI would pretty quickly design for itself. So basically, take those numbers, and multiply them by a certain hard to calculate amount (say 10x due to not being 50k iPhone processors in parallel, and not needing to run transhuman "legacy" functions like a simulated endocrine system or whatever else isn't needed). So far this makes an ASI/hard take offing Seed AI at around 500k human egos generation one. It's going to exponentially increase those numbers with future revisions, so the seed AIs second generation "offspring" will have more like 250,000,000,000 (250 billion) egos worth of power. If we back-convert the 250 billion ego installation it gives a computer volume of nearly 6 olympic swimming pools, so ASIs will pretty quickly become limited by the kind of hardware their installations have on hand, and how much space they can use. Thanks to the speed of light (it takes some noticeable time to get a signal across a 24 meter to a side cube), ASIs probably don't think as anywhere near 250 billion times as fast as a person, but instead can attempt to solve massive sets of problems, approach particularly recondite problems from a billion postman genius points of view, or do other awe-inducing feats of multitasking. The kind of problem which would take the entire human race a million years to solve would take less than an afternoon for a TITAN, Promethean, or Sybil. (abstraction; probably not true) TL:DR ASIs are insanely powerful, really, really insanely powerful. Anyway, this got a little off topic thanks to all the (kind of arbitrary) number crunching, hopefully you all found it interesting. I'd imagine that most of the Prometheans, some of which aren't Seed AI, but are ASI would actually have more trouble downsizing themselves for forking. They'd be native to their own custom hardware, and a very rich computation environment. ADRASTEIA would probably use agents much more than forks because they're native to ASI-dom, while Cassowary and Mycroft who evolved into ASI-dom from a parrot-uplift modeled AGI and an emergent seed AI respectively would be much more fork happy. So I don't think a full promethean would be able to sleeve into a human sized morph, unless they housed themselves in some ASI designed computronium which was greatly more powerful. For example, using a substrate 10 million times more powerful than my calculations of the Myrmidon mainframe a 250 billion ego-equivilant ASI could house itself in a volume similar to that of a human brain. There's some evidence that that kind of computation is possible (The TITAN installation at Iapetus comes to mind, as it could be interpreted as *infinitely* powerful based on Into The White) in Eclipse Phase, so it could happen. Maybe take a page from the Culture and have quantum-foam derived computation if you want to go that route. EDIT: It would take way more than one generation to get to the 250 billion power level. There was an operator error in my math.