My post got eaten by "router? you have a router?" just before leaving for work
EDIT: And isn't Magic that game where it's much easier to do infinite damage than to do a fixed, very large number?
Yes, yes it is.
The combo in question essentially throws stuff onto the stack, then while it's resolving, doubles the amount of stuff on the stack.
Repeatedly.
It is an infinite combo limited by the number of cards you have in hand (which by the time the combo reaches that section, should be 30 cards).
It works by using Kiki Jiki, Minion Mirror, and Doubling Season (as well as Opalescence, making all enchantments--i.e. Doubling Season--creatures) at its core.
The final steps include using Karakas (legendary land) to untap Kiki Jiki. Rootrunner (part of a prior Soulshift combo) to return Kakras to the top of your library, Wargate to play it again (duplicating it a billion times with Minion Mirror and Doubling Seasons, as it counts as a creature thanks to Nature's Revolt). Then Reborn Hope to get the Wargate back, Deja Vu to get the Reborn Hope back, Twincast and Recap to repeat Deja Vu, and finally, Holistic Wisdom to get back Recap.
Each of those spells is also duplicated a billion times when cast due to Mirari (or Rings of Brightearth in the case of Holistic Wisdom), and all of them count as instants due to Vedalken Orrery.
Mana is obtained by sacrificing a tiny fraction of the duplicate permanents created in each step to Phyrexian Alter (or alternatively, playing Black Lotus, letting March of the Machines let it count as a creature, getting it duplicated by Minion Reflector, multiplied by a billion Doubling Seasons, then before Minion Reflector resolves, sacrificing March of the Machines; only the original Black Lotus dies from having 0 toughness, the remainder resolve due to the Last Known Information rule*).
*Here's two very useful points about Minion Reflector triggers. #1 We don't have to pay the 2-mana until we get to the triggered ability on the stack. #2 If the creature Minion Reflector was copying leaves the battlefield before the trigger resolves, it STILL makes a copy using 'Last Known Information'.