A computer that exists in the future
Minimun specs impilies the 'Lowest possible specification to achieve 50-60 FPS, or to get reasonable preformance in the majority of games'.
Well I run a AMD64 3200+ @ 2.2 GHz / 1024MB RAM / GeForce FX5950u and games vary from 4-15 FPS avg, with exceptions comming from TimeSplitters 2 that can jump to 40 FPS in very low poly scenes with no enemies (eg most of the time it runs at 7 FPS), and 2D games.
Whilst the RAM and GPU has very little impact on GameCube emulation under dolphin, the CPU has a huge impact, so aslong as you can run Pixel Shader Model 2.0 on your graphics card, your primary concern would be CPU strength....oh say 8-10GHz should help.
Basically no-one knows the min spec for dolphin as simply the machine doesn't exist yet.