:Central Dome

31.5m2 for each member is quite a lot. here is many functions of that dome and many members. Here is almost no probability to meet all members in dome in the same time. We can calculate on:

Mall for 10k

if we can eliminate shelves and possible lanes between them, we can minimize this to one circular "market street" around whole dome. If that "Mall" will share space with public corridors it is enough to be 3.1m wide (1m to member access to shelve, 0.6m width of shelve, 1.5m area to maintain goods in shelves from back). Here is a possibility to eliminate shelves by using automation. When we use some automated delivery system with screen to choose goods then we need i.e. 100 machines to serve, each have to serve to only 100 members. And the best solution is eliminating screens to choose goods and transferring this task to members communication tool (minipc, tablet, smartphone) and machines can be turn in delivery boxes and stacked.

Rest zones

Library will be very small in this digital era and can be merged with coffee house. Question is how much people will sit here and chat or read books together in the same time

Restaurant could be small place in point of 10k members. I thing, that apartments can be equipped by small kitchens.

Swimming pool will be quite big to 10k people, but it can be outside as lake with bio-cleaning system based on vegetation. Based on weather conditions in place here will be useful to build sauna, cryochamber, mud bath, jacuzzi bath or similar water based relaxation facilities.

School, nursery, education spaces. It could be a small problem, but if schedule of lectures will be established, then we can calculate on needed space. i.e. Auditorium for 50 members needs only 12m width and 4m depth without stage and access lines. Then if we will divide for each lecture 1.5h and will lecture 15h per day we need only 10 auditoriums to serve to 5k of members.

Labs are special topic. It depends on projects. LHC has i.e. diameter measured in kms ;)

and so on...