I understand it as reboot civilization after a disaster that kills everybody else and destroys all technology and collected knowledge. You need at least around

I understand it as reboot civilization after a disaster that kills everybody else and destroys all technology and collected knowledge. You need at least around a thousand people so that you avoid too close family relationships over the generations. Enough women to sustain birthrate over the 2.10 per woman number necessary for population stability. Even more births are necessary in a pre-modern society. At least 90% of your workforce will be involved in obtaining food. The number might be lower under favorable conditions, but have that in mind as a rule of thumb. If your seed population has access to large domesticated animals or source of fish, it will help them concentrate on the main job, a.k.a rebulding civilization. So, the rest of your population will be craftsmen, scientists, industry workers, and administrators that supposedly will facilitate the work of the others. Under administrators we can talk either bureaucrats or traders or whatever people you need for your distribution model. Craftsmen are people who build or obtain stuff that a single person cannot do on their own because it is time-consuming or requires specialized knowledge. This includes carpenters, smiths, farmacists, and so on. If we take ancient cities as an example of relatively independent units that are able to survive more or less on their own, and if we calculate the surrounding villages as food base for the city, with approximate population of a city around 4-5 thousand and 5-10 times more in the villages, the figure will be around 40000-50000 people. This culture must be well-organized, have written tradition, relatively free transfer of knowledge, stable environment, and space to expand. The future generations should be able to use the preserved knowledge for obtaining even more resources and have accelerated expansion. There is a tradeoff here, because the more knowledge you want preserved, the more people and resources should be involved in preserving it, which means more people needed to supply them with food, shelter, and parchment. So, try to keep only the knowledge necessary to build all the rest. Maybe good candidates are: math, logic, scientific method, mechanics, basic chemistry, biology, and astronomy (always good to know what part of the year it is if you want good agriculture). These are all back of the envelope thoughts so might not hold out under careful examination.