[Fred Brackin]

Sorry if it's not the answer you're looking for but in Gurps the answer is "it's never achieved".

The formula for IQ for a Volitional AI is required Complexity equals [(IQ/2)+3].

The highest Complexity in a hard science universe is a TL12 Megaframe with the Genius option for 15.

Complexity 15 equals IQ 24. That's smarter than any natural human but much of the effect is blunted by the rule of 20.

Knowing all skills at 14 or 15 is less than omniscience anyway (and yes, there are no default to attribute Skills). Even with Skills in the 30 you can still only invent things that are physically possible. High IQ does not equal a License to ignore the Laws of Physics.

If you don't like these numbers you'll get generticlally similar ones out of any formula that bases IQ on finite computing resources. The Singularity requires infinte (or possibly only transfinite) computing power.

Transhuman Space does not assume unlimited computing power at any TL. There may be a few years before the majority of people in the setting figure this out but eventualy they will when they notice the Singularity doesn't happen.

Even for dreamers who do assume unlimited computing power at some unavoidable point in the future it's called a "Singularity" because it goes beyond their ability to comprehend.

It's sort of like the Singularities assumed to be at the core of black holes. You reach a place where the equations fill up with infinity symbols and a certain sort of mathematician assumes that Reality breaks down at the point rather than assuming he's reached the limits of his equations.

Anyway, there can be no vision of the Singularity pretty much by definition. It''s called a Singularity because it can't be visualized much less mathematically described.