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clarification
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P.S.

  • You said: "Difference with 10kW or 1GW starting conditions may be like a year or two, so it not so essential." But sorry, I haven't mentioned that, any bit of time would matter in my setting, because there may be chasing enemies behind. Also, basalt fibre is a very good material too. – @Vegetable New Man

I did mention that as characteristic of the process, not that one has to start with 10kW, it just that one can have very little to begin with. But it need to understand it all is a tradeoff - more energy more mass of the setup. You may have a reactor whatever GW's it is, as part of the ship for free, but to convert those GW's to work and parts and production - it requires corresponding amount of equipment. GW's alone is not enough, I would say for every kW you have it 10-100kg of equipment - it also a range, not a fixed number and there will be some difference in time and such.

So it may be more of a question how big are those interstelar ships you have, and how much they can take, rather than how small a setup can be. More you take, faster things unroll, that's for sure, but it maybe have a slower speed of travel and acceleration and as result bigger jorney time and loss of time here.

It more or less all up to you, and your story - as for any problem there is a solution. With a growth rate like a double in a week - the difference between 10kW setup and 1GW one is about 4 month. And if ship has less mass it maybe can be accelerated faster to a higher velocity, and wih 2% difference in resulting speede near 0.1c you may win a year as an example(for a 4ly jorney). And if you consider that most of the mass (which aspect is skipped, by your request, again, I do not assume anything about your story, it up to you, I just consider a typical scenario without magic, and it is up to you which side you shift the knobs) may be one which is needed to deaccelerate at arriving system, and it can be a huge mass - difference can be(or not) very significant, more significant than 4 month.

So in a sense I meant it may be irrelevant for the process - you win in one place lose in another, or vice versa. But I would say smaller is preferale, but not necessarly(as an example when one can't take advantage of that, guarantee safe jorney for that small setup, safety margins are not satisfactory etc) - smaller stuff can be kicked to a higher velocity and it is the main loss/gain of time for interstellar expansion.

Yes, basalt is good, so as gabbro-diabase - both can be cast as metalls, some random paper, just a title not sure what the content of it is, but this direction Evaluation and modification of the initial composition of gabbro-basalt rocks for mineral-fiber fabrication and stone casting

That casting part is interesting, it can replace pure metalls, especially in microgravity, and do so for all kinds of applications. It may have certain disadvantages, but for a rapid bootstrapping those disadvantages may be irrelevant, but advantages what is top importance.

P.S.

  • You said: "Difference with 10kW or 1GW starting conditions may be like a year or two, so it not so essential." But sorry, I haven't mentioned that, any bit of time would matter in my setting, because there may be chasing enemies behind. Also, basalt fibre is a very good material too. – @Vegetable New Man

I did mention that as characteristic of the process, not that one has to start with 10kW, it just that one can have very little to begin with. But it need to understand it all is a tradeoff - more energy more mass of the setup. You may have a reactor whatever GW's it is, as part of the ship for free, but to convert those GW's to work and parts and production - it requires corresponding amount of equipment. GW's alone is not enough, I would say for every kW you have it 10-100kg of equipment - it also a range, not a fixed number and there will be some difference in time and such.

So it may be more of a question how big are those interstelar ships you have, and how much they can take, rather than how small a setup can be. More you take, faster things unroll, that's for sure, but it maybe have a slower speed of travel and acceleration and as result bigger jorney time and loss of time here.

It more or less all up to you, and your story - as for any problem there is a solution. With a growth rate like a double in a week - the difference between 10kW setup and 1GW one is about 4 month. And if ship has less mass it maybe can be accelerated faster to a higher velocity, and wih 2% difference in resulting speede near 0.1c you may win a year as an example(for a 4ly jorney). And if you consider that most of the mass (which aspect is skipped, by your request, again, I do not assume anything about your story, it up to you, I just consider a typical scenario without magic, and it is up to you which side you shift the knobs) may be one which is needed to deaccelerate at arriving system, and it can be a huge mass - difference can be(or not) very significant, more significant than 4 month.

So in a sense I meant it may be irrelevant for the process - you win in one place lose in another, or vice versa. But I would say smaller is preferale, but not necessarly(as an example when one can't take advantage of that, guarantee safe jorney for that small setup, safety margins are not satisfactory etc) - smaller stuff can be kicked to a higher velocity and it is the main loss/gain of time for interstellar expansion.

Yes, basalt is good, so as gabbro-diabase - both can be cast as metalls, some random paper, just a title not sure what the content of it is, but this direction Evaluation and modification of the initial composition of gabbro-basalt rocks for mineral-fiber fabrication and stone casting

That casting part is interesting, it can replace pure metalls, especially in microgravity, and do so for all kinds of applications. It may have certain disadvantages, but for a rapid bootstrapping those disadvantages may be irrelevant, but advantages what is top importance.

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Like the intro of @TheDyingOfLigth answer, especially this part

  • Another thing to consider is that the bootstrapping process you need will be something that has been perfected in the interplanetary age. Von Neumann replicators, which are the technology you are ready asking about, are immensely useful as the basis of any economy. This is what any group building space stations or colonies wants. ... So keep in mind that you aren't using some experimental setup, you are simply using a sports car type Von Neumann maschine relative to the usual economy class ones a typical SEAM setup every colony has, it just that your mass requirements are higher than typicaly(meaning starting from least mass possible).

So yes, it exactly a way to look at the problem. You may even be starting with just regular setup, without any more strict requirements, but one which is typically used to eat out an asteroid.

And here we somewhat get back to that K2 question of yours Lift 10 Billion Tons of Material From a Planet (Every Second) and associated questions/answers, including bootstraping in general (there are some interesting ones Semiconductor foundries are a thing of the past. Rebuild the computer industry if you can and there is more of those bootstraping q's on WB in different settings)

This paper is exactly what you are looking for https://arxiv.org/abs/1612.03238 (Affordable, Rapid Bootstrapping of the Space Industry and Solar System Civilization) as it has exactly the constrains you mention - least amount of mass of that boostraping complex. Unfortunatly it more like concept, which needs more numbers and details and thougths, and it did undervalue the meand of regular production in favor of 3d printing, but it has it both of those considered which makes the work better than many public consideration of replacing everything with 3d printing - great tech, but no need to make it all more complex than it should be, conventional tech works great for conventional stuff. I do recomend to read the work, and maybe even talk with the guy he was available on twitter if I recal correctly. The problem is the same, as constraints are the same. And there is a lot to say on the problem, but it a deept rabbit hole.

100t and mass of your AI is sufficiently reasonable number. 1t may be also a reasonable number, it just harder to validate it, but considering that intro of @TheDyingOfLigth it could be expected. In an extreame - you need a pair of hands, and few tools to make it happen, and some energy source, 10kW is enough, to start the process - so it more like how much a pair of robotic arms mass is plus maybe additional 100kg of equipment and materials to make life easier. Difference with 10kW or 1GW starting conditions may be like a year or two, so it not so essencial.(in a paradigm you accepted, exponential growth of dyson swarm setup)

That potencial of exponential growth is applicable here as well, it just scale is much smaller, but basics are the same - cover your energy needs first with simpliest means posible which grow the fastest, then start then growth of complexity, reshaping available materials for more complex stuff which may be more efficient and opens technology branches, allowing you to clumb to the level of thech you need.

As source of material there is no need to be picky, any sufficiently big rock will do, no need to search gold asteroids or carbon one or those which have enough water, or much iron. Any sufficently big one will do - so you picking 1km diameter one or bigger.

Build your crude energy extractors with traces of iron, you may have in hands or electrolyse from regolith there. Just regular rocks have suprisingly high iron conent - percents - that's enough, so as there Na, K, Ca, Al which can be as good for reflective stuff - so any rock has enough of metals to make colelctors. Many structural parts of every equipment can be that melted regolith - it does not have be that specifically strong in microgravity and basalt and diabase compositions are strong enough for many mechanical purposes. Including heat to mechanical work and to electricity conversion units.

  • so in nonconventional environment, caring about EROEI - conventional materials are not the first goal, and using available materials as is can bring one quite far in that bootsraping process. There may be significant differences depending on average composition, is there water (or somewhat bound hydrogen) or not - all those probably can be handwaved for maturity of that bootstraping technology.

  • I do mean that any rock will do, they are all more or less the same. Also I mean water in abundant quantities is not so important and not required and trace quantities, like on the surface of the moon, it is sufficient. So as other elements even if it traces of them it may be sufficient. But it a big topic, and no need to dive in it too much so say that at least 90% or more of the rocks will do.

Splitting the whole rock, 1km3 one, even if the composition of it isn't best(unlucky one) it should get you to all the modern technologies. So it minimal requirements for a target, and avoid thick water gas shells - they create more problems than solutions(like Ceres one)

Working with plasma and with abundant energy, and we are talking potencially about 400'000 GW here, may be good way to separate all the material in its elements, extracting trace elements etc, which you may need as doping for andvanced CPU's etc. And reaching that does not require current level of computing power, vacuum tubes can do, early transistors can do, early cpu's can do, basic analog electronics can do - so there is an assortment of things to pick from and use as appropriate to comply with available bill of materials, to extend that bill of available materials.

  • just note - insulators can be replaced with SiO2 coating. And making coatings of all kinds is what vacuum good for.

So a workhorse is 1920-1970 tech stack, and when few GW's are reached it may start complication process, for a fraction of that energy, 1-10%, the rest is your workhorse to convert the whole rock into a powerplant, while using 1-10% of energy output for more complex tech preparations, and when done 100% of it for raising tech sofistication to required level.

Then send 100-1'000'000 t payloads to conquer other asteroids you can easily get. Move to a bigger body and start K1,K2 processe and make stations to catch human payloads or to transfer/send resources - energy materials back home. Or whatever.