I believe that the latest Trader change kills the triple up arrow solution. It had a good run. 
I tried to make a replacement for bitwise & paulfc's brilliant 3 up-arrow solution, which now seems invalid due to recent rule changes. I am using Livery & Falconer in place of Black Market & Haggler. But even with Mandarin thrown in, it does not achieve 3 up-arrow growth. It is superior to the other 2 up-arrow solutions in this thread, but it does not lend itself to easy analysis. I am hoping that working together, we may improve upon it.
Kingdom: Squire, Changeling, Black Market, Scavenger, Patron, Falconer, Livery, Scrying Pool, Golem
Black Market: Mandarin, Rogue, Vault, Count, City Quarter, Herbalist
Events: Travelling Fair, Donate
Landmark: Obelisk on Livery
Projects: Capitalism, Academy
Ways: Way of the Seal, Way of the Turtle, Way of the Mouse -> Hermit
Victory points are generated by Obelisk.
Getting started: (in no particular order):
buy 2 Black Markets and then buy all the cards from the Black Market
buy the projects Capitalism and Academy
buy Seaway (using Quarry) and Training for Livery
buy 2 Scavengers
buy lots of Scrying Pools (or alternately Squires and trash them with Donate, gain Scrying Pools)
buy lots of Liveries, Falconers, and Golems
buy Donate to trash unwanted cards
Starting deck
1 Mandarin
1 Herbalist
1 Vault
1 Count
1 Rogue
1 City Quarter
2 Black Markets
2 Scavengers
S Scrying Pools
L Liveries
F Falconers
G Golems
I have denoted the start and end of the Black Market treasure phases, to indicate where I play action/treasures as treasures.
Turn start: (Quarry is in hand, Scrying pool has been set aside as the result of the previous turn)
play Scrying Pool (from Way of the Turtle), draw entire deck (+action)
play Herbalist as Way of the Seal
<begin outer loop>
play Black Market
<begin Black Market treasure phase>
play all Liveries
<end Black Market treasure phase>
<begin Horse gaining loop>
play Falconer, gain Patron
Patron is a four coin card so we gain one Horse for every Livery played this turn (not just those currently in play).
Patron is a card of three types and thus we can react to gaining it by playing another Falconer from our hand.
repeat this sequence for all Falconers thus playing them all with just one action.
(each gained action card comes with +action from Academy. It should be pretty clear by now that we will never run out of actions.)
<end Horse gaining loop>
play Black Market
<begin Black Market treasure phase>
play Quarry
<end Black Market treasure phase>
For all Horses and Patrons we also have in hand,
play <action> as Way of the Mouse (Hermit), gain Livery
(Quarry made 5 coin cards affordable to Hermit, but they do not trigger Liveries to produce Horses.)
(each gained action card comes with +action from Academy.)
play Scrying Pool, draw Horses, Patrons, and Liveries
For all Patrons and all Liveries and all-but-one Horse,
play <action> as Way of the Mouse (Hermit), gain Livery
play Scrying Pool, draw Liveries
<begin main Hermit loop>
For all Liveries,
play Livery as Way of the Mouse (Hermit), gain Livery
play Scrying Pool, draw Liveries
{Exit loop when only 4 Scrying Pools remain, or 5 Scrying Pools if there is only 1 Golem}
<end main Hermit loop>
For all Liveries (one final time),
play Livery as Way of the Mouse (Hermit), gain Falconer
play Livery as Way of the Mouse (Hermit), gain Squire
play Scrying Pool, draw Falconers and Squires
play Vault, draw <two cards>, discard all but Squires, Scavengers, Golem, Mandarin, and <two cards>
play Scavenger, topdeck Scrying Pool
play Scavenger, topdeck Count
play Golem, reveal Count and Scrying Pool
play Count, discard <two cards>, trash hand which is just Mandarin and a lot of Squires, gain Scrying Pools for trashing Squires
play Scrying Pool, draw entire deck (only non-action is Quarry which is in play)
play Rogue, gain Mandarin from trash,
topdeck treasures (Quarry, Black Markets, Liveries, Patrons, Count, Rogue, Vault, Scavengers, Herbalist)
put Quarry and a Black Market on top
play Horse, draw Quarry and a Black Market
play Scrying Pool, draw entire deck (Quarry already in hand)
{Exit outer loop when no Golems remain}
<end outer loop>
play Black Market
play all Liveries
For half of your Falconers,
play Falconer, gain Patron and Horses, convert all to Changelings and discard.
For the remaining Falconers,
play Falconer, gain Patron and Horses, topdeck all
play Scrying Pool. Draws all of the topdecked Patrons and Horses up to the first Changeling
play City Quarter. Draws all of the Changelings.
play last Scrying Pool as Way of the Turtle.
Buy Phase:
play all Patrons
play Herbalist
DO NOT play Quarry
buy Travelling Fair for extra buys as needed
then spend everything on Liveries, gaining a lot of Horses in the process
Night Phase:
exchange the Changelings for Golems
Cleanup:
topdeck the Quarry (by way of Herbalist)
one Scrying Pool has been set aside (by Way of the Turtle)
Proof of finiteness
Liveries in large number are a powerful force. If Horses are allowed to gain more cards that produce Horses unimpeded, unbounded loops are easy to create even without the presence of Mandarin. Add Mandarin and Capitalism and now you have a lot of exploits to plug. The kingdom ended up being very complicated because of it, due to the addition of necessary interlocks. Here's the reasoning why play is bounded.
The case of not purchasing Capitalism.
We have only one Mandarin and one Rogue. To gain the Mandarin, we first have to trash it and then gain it back from the trash with the Rogue. We can trash it easily with Hermit. When we gain the Mandarin back, the only thing going back onto the deck will be the Quarry, so the Rogue cannot be played again and we cannot gain the Mandarin back again. After that, the playing of all cards will be final. Unbounded play must therefore be predicated on gaining more cards during play.
The only gainers are Hermit and Falconer.
Without the Quarry in play, the Hermit is limited to gaining three coin cards and Falconers are limited to gaining four coin cards. The Falconers can therefore produce more Horses. But the number of Falconers in our deck is finite and will run out. After which we can play actions as a Hermit and only gain cards that cost up to three coins which will not produce any more Horses.
With the Quarry in play, five coin actions are reduced to a cost of three coins and can be gained with Hermit, but they will not produce more Horses. We can gain more Falconers, but they are limited to gaining cards which cost less than themselves, and their cost has been reduced to three coins. Eventually we will not be able to gain any more cards.
There is one final way to gain a card; trashing a Squire. The Rogue is an attack card, but it is not in the supply, so we can only gain Scrying Pools.
Any action played as a Hermit can gain a Squire and trash a Squire and gain a Scrying Pool. That seems like a gain, but it isn't. You are losing two cards and gaining two cards. It just makes waiting for the end take a lot longer.
The case of purchasing Capitalism.
Hermit can no longer trash the Mandarin, nor the Squires. The gaining situation is the same as above. We can gain Horses only when the Quarry is not in play, but we cannot gain any really useful cards unless the Quarry is in play. Gaining the Mandarin from the trash will return the Rogue and a lot of other useful action/treasures to the stack to be played again but most importantly, it removes the Quarry from play. The only card that can trash the Mandarin is the Count and only by trashing the entire hand. That obviously ends play unless triggered by a Golem. This is limited because Golems are not treasures and they cannot be returned from play and they cannot be gained, only acquired in the Night phase or bought in the final Buy phase.
Analysis
If we play L Liveries and then F Falconers gaining F Patrons, we will gain L*F Horses.
We then turn those L*F Horses and F Patrons into (L+1)*F more Liveries,
and then turn those Liveries into more Liveries, S-4 more times for O(L*F*S) Liveries.
The final Hermit loop converts O(L*F) Liveries into O(L*F*r) Falconers and O(L*F*(1-r)) Squires. The Squires are converted to Scrying Pools by the Count.
For the next playing of Falconers, L' = O(L*F*S), F' = O(L*F*r), and S' = O(L*F*(1-r)).
To maximize Liveries gained next iteration, we need to maximize L'*F'*S'= O(L*F*S) * O(L*F*r) * O(L*F*(1-r)) = O(L^3*F^3*S*(1-r)*r).
That at least tells us that we should gain Falconers and Squires in equal number so F = S, and that equates to O(L^3*F^4).
The number of Liveries appears to cube itself each time we play a Golem, but not really since the other components do not grow nearly as fast.
Empirical data suggests that the actual exponent of growth for Liveries is ~2.4 (though my spreadsheet could only do 7 iterations before blowing up).
This is repeated for each Golem, with the number of Golems for the next turn equal to half the number of Horses gnerated in the last iteration.
Empirically, G' = ~(L^(2.4*G)^1.7. That means that overall growth per turn = L^(2.4*[(L^(2.4*G)^1.7]) or thereabouts not even counting the Liveries we end up buying.
The problem is that the exponents aren't in a favorable place. I believe, overall, it surpasses 2 up-arrows.
For those that are new to up-arrow notation:
If f(x) = x*2, then f(f(f(2)))) = 2*2*2*2 = 2^4 = 2↑4 = 16 "exponentiation"
If f(x) = x^2, then f(f(f(2)))) = ((2^2)^2)^2 = 2^8 = 256
If f(x) = 2^x, then f(f(f(2)))) = 2^(2^(2^2)) = 2↑↑4 = 65536 "tetration"
If f(x) = 2↑↑x, then f(f(f(2)))) = 2↑↑(2↑↑(2↑↑2) = 2↑↑↑4 = ? "pentation"
Mathematicians have not blessed that second row with a name that I could find.
Bankers would call it "compounding", and if applied to finance, "amortization".EDIT: Forget what I said about amortization. It's just another form of exponentiation. I don't have any label for that second row.
