Power Artifact/Mana Vault........?

[Metabubbles]

Should I assume this will effectively give me infinite mana?  Also if it does can I Stroke of Genius my opponent during my upkeep for the win?  And if not, can I cycle my decree of justice?  Thanks.

[Toad]

Text (5th+errata): ~this~ doesn't untap during your untap step. ; At the beginning of your upkeep, you may pay . If you do, untap ~this~. ; At the beginning of your draw step, if ~this~ is tapped, it deals 1 damage to you. ; : Add to your mana pool. [Oracle 2003/07/01]

The untap ability is a triggered ability. You can only use it once per turn. So your combo doesn't work. It does with Grim Monolith though.

[DEA]

you can also do it with basalt monolith if you have a mana filter like bog initiate