When the Precursor Golems trigger (and don't forget that you also have 16,781,312 vanilla Golem tokens), the first trigger to resolve creates some copies. If the copies targeting DS resolve first, then you go to 2059, then 2^2059, and so on, ending at 2^^4099. This is not the same as 2 -> 2 -> 4099, but rather 2 -> 4099 -> 2. (In this case, the latter expression is larger because the first one is just 4, but when numbers bigger than 2 are involved, small -> small -> big is for greater than small -> big -> small.
The second Precursor trigger now sees about 2^^4099 creatures to distribute copies too, and at the end of that, you go to 2^^(2^^4099). Each subsequent trigger merely adds a 2^^( in front of that expression, but since each set of ^^ is in a separate parenthetical expression, you can't just merge all the arrows together; they're simply racking up iterations one by one at a certain level of recursion. When the stack finally clears, that puts you at about 2^^^4098, which is 2 -> 4098 -> 3, a far cry from anything involving 45,000 up arrows.
A second Heat Shimmer would put you around 2^^^^4 (2->4->4), and if you devote any more slots to token-making effects, they each increase the second number in that expression by just one, and don't affect the third number at all. Going higher than that requires a way to dynamically produce some number of Heat Shimmer plays that's commensurate with everything you've already done. One way of doing this would involve playing Gaea's Cradle once you've used up all your other resources to lock in a particular amount of mana, and then Tasigur, the Golden Fang to repeatedly get the card back from your graveyard. But then you'd be hard pressed to extend anything beyond that.
In order for first strike lifelink to help, we need to have an attacker that both a) has some way of getting bigger proportional to the number of creatures (because the set of attackers is locked in), and b) will never leave combat. If March of the Machines goes away for any amount of time, an animated artifact is excluded by b), as is any creature whose original representative keeps cycling in and out because of Dual Nature's wipeout clause. Whatever the current working list is, do we have a usable candidate for that?
With just one Dual Nature and its token, we can do this:
-Play Changeling Titan for the first time. Champion and 2 token-making triggers go on the stack.
-Let Champion happen first. Pick up Mana Crypt, which needs to be animated. All Mana Crypt tokens are erased, not that this is important.
-Create a token CT1, and champion CT.
-Dual Nature and CT both get their "leave" triggers.
-Return Mana Crypt first. 2 Dual Natures trigger on this, creating 2 extra Crypt tokens.
-Dual Nature's trigger wipes out CT1.
-CT returns. Champion and 2 token-making triggers go on the stack.
-Let Champion happen first again. Pick up March of the Machines, and Dual Nature wipes out any tokens it might have had.
-The Crypts are now deanimated and can tap for 6 colorless mana.
-Create another token of CT and champion the original...
So this is already enough to get unlimited colorless mana and other effects that require tapping noncreature artifacts. It can also flicker anything else repeatedly, but their numbers will remain stable at 1 plus the number of Dual Natures in existence so that doesn't make progress. Increasing that number is then the base goal, and doing that requires bouncing or championing it, bringing it back before it can wipe out its own tokens, then intervening with another effect that can target it in response to its own ETB trigger. That results in doubling the number of DNs that stick around, from which we can bump up the population of Bloodbond March, Psychic Battle, and the artifacts.
Note that one of the options for champion is always "sacrifice this creature", which can put it on Mimic Vat with no outside help and allow us to create a token copy (with haste) and champion something at any time. As long as we require using up a Bloodbond March to bring the original back after that, though, this doesn't break anything.
Suppose we have Dual Nature which makes a token copy of itself, DN1. Then Copy Enchantment gets two triggers which make DN2 and DN3, for a total of four Dual Natures.
Now Changeling Titan comes in and pick up those four triggers, as well as a champion trigger. Choose to champion Copy Enchantment first of all, then the first Dual Nature trigger creates CT1.
The trick is, CT1 can champion the original Changeling Titan itself. That brings back Copy Enchantment, getting four more Dual Natures to go to 8, and it also triggers the Dual Nature abilities to wipe out all Changeling Titan tokens. CT1 goes away, returning original CT from champion, now on a board with 8 Dual Natures.
Obviously, this can be repeated forever, doubling the number of Dual Nature tokens each time. So this setup doesn't work.
Even if Dual Nature didn't have that trigger on anything LTB, it would still be forbidden because the second Dual Nature trigger creates CT2, championing CT1 and returning CT.
Parallel Evolution produces copies of the highest permanents, with haste, at the lowest stage. Even with that setup rendering it impossible to have any tokens of Mimic Vat at all, the ability to make a new Karplusan Yeti (in fact, several of them) for every 4GGG, along with more copies of Mirror of Fate to get back the flashback card for the next cycle, is way too good.
I just noticed: when the sequence gets up to a black Paragon, we can get rid of Dralnu's Crusade so the goblins don't get a boost, but Royal Assassin is inescapably black, and will be too big to be the target as the next step down. So that still leaves a bit of a gap, and there's no drop-in substitute for Royal Assassin that's doesn't have its own problems.
Lots of complicated math and boldly taking Magic cards to places where none have gone before.
You might try looking over the most recent published version of the article to get the hang of the kinds of things we're looking for cards to do, but ever since a breakthrough on page 2 of the topic (post #41), the deck has been going in a different direction, such that a lot of the cards that hold up the structure shown on that page, wouldn't even be safe in the new outline--chief among them Doubling Season itself.
Beyond that, Spirits are too early in that outline. Specifically, they're before black mana, so by hitting Horobi with Urgent Exorcism and putting it on Mimic Vat, we get black mana out of sequence.
Note that the original incarnation of the deck name was no doubt inspired by the apt inclusion of Blasphemous Act, which served as board control and as a way to deal a ton of damage to your own Boros Reckoner.
Does Weaver of Lies even complete its step? In order for the original to be targeted and reused, a token copy will have to turn face up (it only targets other creatures with morph). But the only way a token can be face down is if a morph trigger actually resolves. That far down, we can make Cowardice go away, but there's no way to clear out Horobi, so it doesn't seem like anything will actually be able to turn face down from it.
Per the challenge rules, deck size is fixed at 60, so you would have at most 53 cards to fetch unless you're doing some graveyard reshuffling. However, due to mana constraints, you can't actually play all those cards off the opening hand alone. The closest you get is Lotus for GGG, Petal for W, play Knight and Crossroads, then Bayou for B and Dark Ritual allows you to float 3 mana when you activate Knight for the first time. That lets you go get a Tundra or something, which you can finally tap for U to play Retreat, but by then the Knight is tapped and it is no longer possible to get any landfall triggers for Retreat to witness. Hence, the actual damage you can get out of that hand is 2.
If you read over the existing publication, it uses a step that can be repeated as much as desired, in a similar fashion, except that the opponent has to draw a card each time through and their deck size is fixed at 60 as well. That mechanism, though, is good for a lot more than one additional power each time through the loop.
Skull of Orm would be better served as Crystal Chimes: in addition to potentially bringing back multiple cards at once (Bloodbond March + Psychic Battle), it also costs 3 to use instead of 5, which makes getting off the ground significantly more palatable.
The second Precursor trigger now sees about 2^^4099 creatures to distribute copies too, and at the end of that, you go to 2^^(2^^4099). Each subsequent trigger merely adds a 2^^( in front of that expression, but since each set of ^^ is in a separate parenthetical expression, you can't just merge all the arrows together; they're simply racking up iterations one by one at a certain level of recursion. When the stack finally clears, that puts you at about 2^^^4098, which is 2 -> 4098 -> 3, a far cry from anything involving 45,000 up arrows.
A second Heat Shimmer would put you around 2^^^^4 (2->4->4), and if you devote any more slots to token-making effects, they each increase the second number in that expression by just one, and don't affect the third number at all. Going higher than that requires a way to dynamically produce some number of Heat Shimmer plays that's commensurate with everything you've already done. One way of doing this would involve playing Gaea's Cradle once you've used up all your other resources to lock in a particular amount of mana, and then Tasigur, the Golden Fang to repeatedly get the card back from your graveyard. But then you'd be hard pressed to extend anything beyond that.
-Play Changeling Titan for the first time. Champion and 2 token-making triggers go on the stack.
-Let Champion happen first. Pick up Mana Crypt, which needs to be animated. All Mana Crypt tokens are erased, not that this is important.
-Create a token CT1, and champion CT.
-Dual Nature and CT both get their "leave" triggers.
-Return Mana Crypt first. 2 Dual Natures trigger on this, creating 2 extra Crypt tokens.
-Dual Nature's trigger wipes out CT1.
-CT returns. Champion and 2 token-making triggers go on the stack.
-Let Champion happen first again. Pick up March of the Machines, and Dual Nature wipes out any tokens it might have had.
-The Crypts are now deanimated and can tap for 6 colorless mana.
-Create another token of CT and champion the original...
So this is already enough to get unlimited colorless mana and other effects that require tapping noncreature artifacts. It can also flicker anything else repeatedly, but their numbers will remain stable at 1 plus the number of Dual Natures in existence so that doesn't make progress. Increasing that number is then the base goal, and doing that requires bouncing or championing it, bringing it back before it can wipe out its own tokens, then intervening with another effect that can target it in response to its own ETB trigger. That results in doubling the number of DNs that stick around, from which we can bump up the population of Bloodbond March, Psychic Battle, and the artifacts.
Note that one of the options for champion is always "sacrifice this creature", which can put it on Mimic Vat with no outside help and allow us to create a token copy (with haste) and champion something at any time. As long as we require using up a Bloodbond March to bring the original back after that, though, this doesn't break anything.
Now Changeling Titan comes in and pick up those four triggers, as well as a champion trigger. Choose to champion Copy Enchantment first of all, then the first Dual Nature trigger creates CT1.
The trick is, CT1 can champion the original Changeling Titan itself. That brings back Copy Enchantment, getting four more Dual Natures to go to 8, and it also triggers the Dual Nature abilities to wipe out all Changeling Titan tokens. CT1 goes away, returning original CT from champion, now on a board with 8 Dual Natures.
Obviously, this can be repeated forever, doubling the number of Dual Nature tokens each time. So this setup doesn't work.
Even if Dual Nature didn't have that trigger on anything LTB, it would still be forbidden because the second Dual Nature trigger creates CT2, championing CT1 and returning CT.
You might try looking over the most recent published version of the article to get the hang of the kinds of things we're looking for cards to do, but ever since a breakthrough on page 2 of the topic (post #41), the deck has been going in a different direction, such that a lot of the cards that hold up the structure shown on that page, wouldn't even be safe in the new outline--chief among them Doubling Season itself.
If you read over the existing publication, it uses a step that can be repeated as much as desired, in a similar fashion, except that the opponent has to draw a card each time through and their deck size is fixed at 60 as well. That mechanism, though, is good for a lot more than one additional power each time through the loop.