Annualized Geo-Solar (AGS )
See attached concept drawing.
This is same basic concept as PAHS except uses more standard housing and the space under the house as the thermal storage mass. It requires an umbrella around house to thermally isolate the under house area but less (6-8 ft rather than 20 ft). It also has more control in the thermal heating as it controls when heating occurs by routing air flow through mass when desired. (although seems like PAHS was evolving this way also).
This could be applied to a standard dome with a chain shell cover with air gap. Simply draw air under chain shell when sun out (solar powered fan) to center of dome roof then down to floor level and to under slab distributed pipes and out into room (need external exhaust pipe to outside).
Reverse air flow in summer - cool outside through floor pipe and then out through dome shell, cooling shell.
I VOTE for simplicity of no pipes and use exposed concrete as solar gain and cover up in summer with vines and insulate areas to tune performance. The thermal insulated & water proof umbrella seems to be the common important element. As the cooling function comes from the earth below and heat from trapping under umbrella. Wood heat backup seems more practical for heat as climate is too variable. Cooling from ground sync has shown to work in first two domes.
No pipes as above choice makes solar gain direct coupled through dome structure. Air flow system allows some control over heat transfer process. Summer it can flow under floor (cooling air) through dome to roof and out through concrete heater before flowing through side berm soil for summer heat build up. This is reversed for winter so outside air flows though side bermed soil (heated up slightly) then through concrete heater (major heat up when sun out) through dome to floor (heat floor slightly and garden if routed under garden) and out. Flowing through dome guarantees ventilation all year round.
Bottom line: Pipe/air system adds complexity but also thermal decoupling and ventilation. Should try on one unit. Leave unit uninsulated except for south exposed end where a solar heater can be made by insulating dome shell and adding outer concrete shell over insulation with air flow through pipes. One dome air entrance/exit is under foundation/floor and the other is in the ceiling to the solar heater and then surrounding soil berm.