Time Studies

Time Studies are special powerful upgrades bought with Time Theorems, which are bought with increasing amounts of Antimatter, Infinity Points, and Eternity Points.
Resource 	Base Cost	Cost Scaling (multiplicative)
Antimatter 	1e20000 	1e20000
Infinity Points	1 	1e100
Eternity Points	1 	2
As Eternity Challenges are connected to the tree, some information about them can be found here too.
A study that requires a certain challenge may be purchased once the challenge has been first cleared, without needing to purchase the challenge.
A study with a pre-requisite preceded by a dash (ex. 71) means that you cannot purchase the study if the dashed pre-requisite is owned, unless you have a dilation upgrade (71-103) or enough Space Theorems (Studies below 111).
Upon reaching 1e15 dilated time, it is possible to passively generate Time Theorems.
Triad Studies are special Time Studies which comes after Reality, which costs Space Theorems, instead of Time Theorems.
There are 4 Triad Studies, their IDs are 301-304. All studies that costs Space Theorem are listed with base cost.
Exclusively in The Nameless Ones' Reality, there is a secret study to the right of 11 that gives 100 TT when bought.
ID 	Prerequisites 	Description 	Details 	Extra 	Cost (TT) 	Min Total Cost
s 	 	Unlocks a secret achievement (Go study in real life instead) 	This study, and the path to it, is invisible until purchased.
On mobile, tap this study to hide this study and the path to it.
On the Reality Update, Double-click this study to hide this study and the path to it.
While there's a path leading to it from 11, it does not actually require it.	 	0 	0
11 	 	Tickspeed affects 1st Time Dimension with reduced effect 	min(1/(A0.005*0.95+A0.0003*0.05),1e2500)
where A = tickspeed/1000 	This hits the cap at 4.64e-8,333,334 tickspeed. 	1 	1
12 	 	... you ... have great potential ... 	This study, and the path to it, is invisible until purchased.
Exclusive to The Nameless Ones' Reality
While there's a path leading to it from 11, it does not actually require it.	Gives 100 TT (subtracting -100 equals +100) 	-100 	0
21 	11 	Replicanti multiplier formula is better (log2(x)^2 -> x^0.032) 	log2(x)2+x0.032 	The increase kicks in (although very little) at about 1e96, and ends with about a 6,975x higher multiplier at 1.8e308. 	3 	4
31 	21 	Powers up bonuses that are based on your infinited stat 	Affects the 5 infinity upgrades, Eternity Challenge 10's boost/reward, achievement 116's reward, and Effarig's Infinity's reward. 	Infinited^4 	3 	7
41 	31 	Each galaxy gives a 1.2x multiplier on IP gained. 	 	1.2^galaxies 	4 	11
22 	11 	Replicanti interval limit 50ms -> 1ms 	 	 	2 	3
33 	22 	You keep half of your replicanti galaxies on infinity 	Rounds down, but appears to round up if you crunch while on infinite replicanti causing it to autobuy a galaxy straight away. 	 	2 	6
32 	22 	You gain more infinities based on Dimension Boosts. 	max(b,1)
where b = dimension boosts 	 	2 	5
42 	32 	Galaxy requirement goes up 52 8ths instead of 60. 	After galaxies become distant, difference is simply 8 less than normal.
After galaxies become remote, difference is 8*1.002(g-800) less than normal. 	 	6 	11
EC5 	42 	Galaxy cost increase scaling starts instantly (Normally at 100 galaxies).
Dimension boost costs scaling is massively increased. 	 	 	130 	141
51 	41 or 42 	You gain 1e15x more IP 	 	 	3 	14
61 	51 	You gain 15x more EP 	 	 	3 	17
62 	42, EC5 	You gain replicanti 3 times faster 	 	 	3 	17
71(Antimatter Dims) 	61 (-72 -73)/(201 -72/-73)	Sacrifice affects all other normal dimensions with reduced effect 	min(x0.25,1e210,000) (non-8ths only) 	This hits the cap at 1e840,000 sacrifice bonus.
(shows 1e210,000x) 	4 	21
81(Antimatter Dims) 	71 	Dimensional boost power becomes x10 	 	This is better than study 82 when you have less than 1498 Dimension Boosts, before EC2 (after EC2, study 82 is generally more powerful). 	4 	25
91(Antimatter Dims) 	81 	Normal dimensions gain a multiplier based on time spent this eternity 	10min(eternity time(s),1800)/6 	 	4 	29
101(Antimatter Dims)	91 	Replicantis give multiplier to normal dims equal to their amount. 	replicanti 	 	4 	33
72(Infinity Dims) 	61 (-71 -73)/(201 -71/-73)	Sacrifice affects 4th Infinity Dimension with greatly reduced effect 	min(x0.04,1e30000) 	This hits the cap at 1e750,000 sacrifice bonus.
(shows 1e30000x) 	6 	6
82(Infinity Dims) 	72 	Dimensional boosts affect Infinity Dimensions 	min(1.0000109Dimension Boosts^2,1e80000) 	This hits the cap at 130,000 Dimension Boosts. 	6 	29
92(Infinity Dims) 	82 	Infinity dimensions gain a multiplier based on fastest eternity time 	260/max(eternity time(s),2) 	 	5 	34
102(Infinity Dims) 	92 	Replicanti galaxies power replicanti multiplier 	5n 	 	6 	40
73(Time Dims) 	61 (-71 -72)/(201 -71/-72)	Sacrifice affects 3rd Time Dimension with greatly reduced effect 	min(n0.005,1e1300) 	This hits the cap at 1e260,000 sacrifice bonus.
(shows 1e1300x) 	5 	22
83(Time Dims) 	73 	Dimension boosts are 0.04% more effective for each tick upgrade gained from Time Dimensions 	compounding on itself, cap at 1e30x 	This is better than study 81 if you have 7.378381e283 time shards (1.311444e222 with study 171). 	5 	27
93(Time Dims) 	83 	Time dimensions gain a multiplier based on tick upgrades gained from them 	max(n0.25,1) 	 	7 	34
103(Time Dims) 	93 	Time dimensions gain a multiplier equal to replicanti galaxy amount 	 	 	6 	40
111 	101/102/103 	Make the IP formula better 	See Breaking Infinity for the IP formula. 	This increases the OoM of IP gained by about 8.07%. Formula becomes log(x)/285. 	12 	45
EC7 	111 	First Time Dimension produces Eighth Infinity Dimension, and First
Infinity Dimension produces Seventh Dimensions. Tickspeed affects
all dimensions normally.	 	 	115 	160
121(Active) 	111 -122 -123 	You gain more EP based on how fast you last ten Eternities are (real time) 	max(1,min(250/x,50))
where x = average time of your last 10 eternities in seconds 	This is better than 35x at an average time of 7 seconds or less. It reaches a cap of 50x at 5 seconds or less. It reaches 1x around 250 seconds. 	9 (and 2 Space Theorems if not chosen first) 	54
EC6 	121 	You can't gain galaxies normally, but the cost of upgrading your max
replicanti galaxies is massively reduced. 	 	 	85 	139
131(Active) 	121 -132 -133 	Automatic replicanti galaxies are disabled, but you can get 50% more 	 	This is the best boost in this row, especally with Infinity Dimensions path.
The downside "Automatic replicanti galaxies are disabled" is removed with Achievement 138 	5 (and 8 Space Theorems if not chosen first) 	59
141(Active) 	131 -142 -143 	Multiplier to IP, decaying over this infinity 	max(1,1e45/15ln(A)*A^0.125)
where A = infinity time in seconds * 10 	This is the best multiplier in this row for infinities less than 115 seconds. This effect caps at 3326 seconds (55:26). 	4 (and 2 Space Theorems if not chosen first) 	63
122(Passive) 	111 -121 -123 	You gain 35x more EP 	 	 	9 (and 2 Space Theorems if not chosen first) 	54
132(Passive) 	122 -131 -133 	Replicanti galaxies are 40% stronger and Replicanti are 1.5x faster 	 	 	5 (and 8 Space Theorems if not chosen first) 	59
142(Passive) 	132 -141 -143 	You gain 1e25x more IP 	 	This is the best multiplier in this row for infinities between 115 and 272 seconds. 	4 (and 2 Space Theorems if not chosen first) 	63
123(Idle) 	111 -121 -122 	You gain more EP based on time spent this eternity 	(time (s)*1.39)0.5 
(This has a negative effect if time spent in eternity is 719 ms or less (exactly 1000/1.39 ms).) 	This is better than 35x if you spend longer than 881 seconds (14:41) per eternity. It's the best in this row if your eternity is longer than 1799 seconds (29:59). 	9 (and 2 Space Theorems if not chosen first) 	54
EC8 	123 	You can only upgrade Infinity Dimensions 50 times, and Replicanti
upgrades 40 times. 	 	 	115 	169
133(Idle) 	123 -131 -132 	Replicanti are 10x slower until infinity, but their galaxies are 50% stronger 	See Replicanti for slowdown exceptions. Galaxy boost only affects Replicanti Galaxies. 	"Replicanti are 10x slower until infinity" is removed with Achievement 138 	5 (and 8 Space Theorems if not chosen first) 	59
143(Idle) 	133 -141 -142 	Multiplier to IP, increasing over this infinity 	15ln(A)*A^0.125where A = infinity time in seconds * 10
(This has a negative effect if time spent in infinity is 100 ms or less) 	This is the best multiplier in this row for infinities longer than 272 seconds (~6 minutes). It's growth rate is exponential and it will usually always be better to let it sit longer, bear in mind, other factors can influence or even undo a lot of inital growth, so it may sometimes be better to eternity (i.e. Time dimension growth slowing down)	4 (and 2 Space Theorems if not chosen first) 	63
EC4 	143 	All infinitied stat multipliers and generators are disabled. 	 	 	70 	133
151 	141/142/143 	1e4x multiplier on all Time dimensions 	 	This is another 129.2 tickspeed upgrades. (165.1 with study 171) 	8 	71
EC9 	151 	You can't buy tickspeed upgrades. Infinity power instead multiplies
time dimensions with greatly reduced effect. 	 	 	415 	486
161 	151 	1e616x multiplier on all normal dimensions 	 	 	7 	78
162 	151 	1e11x multiplier on all Infinity dimensions 	 	Both boosts in this row are equal, until EC2 makes this one better. 	7 	78
171 	161/162 	Time shard requirement for the next tickspeed upgrade goes up slower 	33% -> 25% (Time Dimensions) 	This will get you about 27.8% more tickspeed upgrades from time shards. 	15 	93
EC1 	171 	Time Dimensions are disabled. 	After EC1R, EC2R, and EC3R, this study goes to the left of 181. 	 	30 	123
EC2 	171 	Infinity Dimensions are disabled. 	After EC1R, EC2R, and EC3R, this study goes above EC3 on web and steam, and goes in between 161 and 162 on mobile. 	 	35 	128
EC3 	171 	Dimensions 5-8 don't produce anything. Dimensional sacrifice is disabled. 	After EC1R, EC2R, and EC3R, this study goes to the right of 181. 	 	40 	133
181 	171 EC1 EC2 EC3 	You gain 1% of your IP gained on crunch each second. 	IP to be gained on crunch. Note that you still generate IP below Infinity antimatter (how much you would be able to gain on crunch if you could crunch).	 	200 	293
EC10 	181 	Time Dimensions and Infinity Dimensions are disabled. You gain an
immense boost from infinitied stat to normal dimensions (infinitied^1000)	 	 	550 	843
192 	181 EC10 	You can get beyond 1.80e308 replicantis, but the interval is increased the more you have 	See Replicanti 	 	730 	1,023
201 	192 	Pick another path from the first split 	Allows you to have 2 paths from the first 3 way split. 	 	900 	1,923
191 	181 EC10 	After eternity you permanently keep 5% of your infinities 	You need this study to bank infinities, but you can use banked infinities without it. "Banked infinities" in any context refers to this study's effect. 	 	500 	793
211 	191 	Dimensional boost requirement scaling is reduced by 5 	 	 	120 	913
221(Light) 	211 -222 	Dimension Boosts affect time dimensions with reduced power. 	1.0025(Dimension Boosts) 	 	900 (and 4 Space Theorems if you have Study 222)	1,813
222(Dark) 	211 -221 	Dimensional boost costs scale by another 2 less. 	 	 	900 (and 4 Space Theorems if you have Study 221)	1,813
231(Light) 	221/222 -232 	Dimension boosts are more effective based on their amount. 	(Dimension Boosts)0.3 	 	500 (and 5 Space Theorems if you have Study 232)	2,313
301(Triad) 	221 222 231 	Time Study 231 improves the effect of Time Study 221 	TS221 effect^(TS231 effect-1) 	 	12 Space Theorems (unlock at V Level 6) 	3,213
212 	191 	All Galaxies are more effective based on your timeshards 	min(log2(time shards)0.005, 1.1) 	This hits the cap at 2.575e57,167,184 time shards. 	150 	943
223(Light) 	212 -224 	Galaxy cost scaling starts 7 galaxies later. 	 	This is better than 224 if you have less than 14,000 dimboosts. 	900 (and 4 Space Theorems if you have Study 224)	1,843
224(Dark) 	212 -223 	Galaxy cost scaling starts 1 galaxy later for every 2000 dimensional boosts. 	rounded down 	This is better than 223 if you have more than 14,000 dimboosts. 	900 (and 4 Space Theorems if you have Study 223)	1,843
232(Dark) 	223/224 -231 	All Galaxies are more effective based on Antimatter Galaxies. 	(1+galaxies/1000)0.2 	 	500 (and 5 Space Theorems if you have Study 231)	2,343
302(Triad) 	223 224 232 	Distant Galaxy scaling threshold starts another 3,000 Antimatter Galaxies later 	 	 	12 Space Theorems (unlock at V Level 12) 	3,243
EC11 	231/232 71 -201 	All dimension multipliers are disabled except for the multipliers
from Infinity power and dimension boosts (to normal dimensions) 	 	 	1 	2,344
193 	181 EC10 	Normal dimension boost based on eternities 	min(1.03eternities,1e13000) 	This caps at 1,012,680 eternities. 	300 	593
213 	193 	You gain replicanti 20 times faster 	 	 	200 	793
225(Light) 	213 -226 	You gain extra RGs based on your Replicanti 	floor(log(replicanti)/1000) 	 	900 (and 4 Space Theorems if you have Study 226)	1,693
226(Dark) 	213 -225 	You gain extra RGs based on their max 	floor((max RGs)/15)
Study 131 does not affect this study. 	 	900 (and 4 Space Theorems if you have Study 225)	1,693
233(Light) 	225/226 -234 	Max replicanti galaxy cost is reduced based on replicanti amount. 	/(replicanti)0.3 	This effect is about x3e92 at infinity replicanti. (300 NVg for standard notation users) 	500 (and 5 Space Theorems if you have Study 234)	2,193
303(Triad) 	225 226 233 	Gain 50% more extra Replicanti Galaxies from Time Studies 225 and 226, and from Effarig's Infinity 	 	 	12 Space Theorems (unlock at V Level 18) 	3,093
214 	193 	Sacrifice boosts the 8th dimension even more 	min(S8,1e46000)*min(S1.1,e125000)
where S = your sacrifice multiplier 	This hits the first cap at 1e5750 sacrifice bonus. This hits the second cap at 2.3e113,636 sacrifice bonus.
(displays 1e125,000x as the cap) 	120 	713
227(Light) 	214 -228 	Sacrifice affects the 4th Time Dimension with reduced effect. 	log(sacrifice bonus)10 	 	900 (and 4 Space Theorems if you have Study 228)	1,613
228(Dark) 	214 -227 	Sacrifice scales better. 	See Dimensional Sacrifice 	 	900 (and 4 Space Theorems if you have Study 227)	1,613
234(Dark) 	227/228 -233 	Sacrifice boosts First Dimension. 	(sacrifice bonus) 	 	500 (and 5 Space Theorems if you have Study 233)	2,113
304(Triad) 	227 228 234 	Dimensional Sacrifice multiplier is squared 	 	 	12 Space Theorems (unlock at V Level 24) 	3,013
EC12 	233/234 73 -201 	The game runs 1000x slower. Failing to get the IP requirement will lead to a similar effect to having too many infinities in EC4.	 	 	1 	2,121
d1 	231/232/233/234, EC11x5 EC12x5
12,900 total TT	Unlock Time Dilation 	When you buy this time study or any of time studies below, it will be permanently bought.
Additionally, after DILR is purchased, the EC11, EC12, and total TT requirement is removed.	 	5,000 	12,900
d2 	d1 	Unlock the 5th Time Dimension 	 	 	1,000,000 	1,012,900
d3 	d2 	Unlock the 6th Time Dimension 	 	 	10,000,000 	11,012,900
d4 	d3 	Unlock the 7th Time Dimension 	 	 	100,000,000 	111,012,900
d5 	d4 	Unlock the 8th Time Dimension 	 	 	1,000,000,000 	1,111,012,900
d6 	d5
1e4000 EP
First 13 rows of achievements	Unlock Reality 	See Reality
Additionally, after START is purchased, the achievement requirement is removed. 	 	1 	1,111,012,901
==Time Study Tree==
Time studies are arranged in a top-to-bottom branching way, such that purchasing any given study gives you the choice of purchasing the next study (or studies) just below it. Each box in the tree is either a time study which will provide a boost, or an Eternity Challenge which must be purchased in order to enter it, and all the boxes cost Time Theorems to unlock.
The tree can be freely respecced at the beginning of each eternity, which can be done by pressing the button at the top of the page. Activating the respec removes all of your purchased time studies and refunds all the Time Theorems spent with no extra cost.
For each of the two-way splits, you can purchase both options if you have enough Time Theorems to afford them. This is also true for all of the studies in the bottom four rows of the tree.
For the first two three-way splits, purchasing the first study of each branch will lock up the other two choices, making them un-purchasable until a respec. The third three-way split requires you to complete all three of those challenges before being able to go farther.
==Eternity Challenges==
Main article: Eternity Challenges
Eternity challenges have two requirements, one being the Time Theorem cost and the other being something else that depends on the challenge (eg. a minimum number of infinities, a certain number of galaxies, etc.). The additional requirement must be met before the challenge can be purchased, which then of course still requires Time Theorems. This means that to unlock EC5 (for example) you need to reach the specified number of galaxies with an extra 130 Theorems in order to purchase it.
Once purchased, the secondary requirement is removed (except for EC11 and EC12) until you either complete the challenge or purchase a different one. The practical upshot of this is that you can now respec the tree without needing to re-do the secondary requirement again, meaning that you can try taking different sets of studies into a challenge if you can't do it the first time around. Note that purchasing the eternity challenge box itself is still required to enter.
After a challenge is completed, it is considered purchased for the sake of allowing later studies to be purchased. This means, for example, that you can get the triple replicanti speed study after completing EC5 (for the first time) without spending 130 Theorems on the EC study. However, you still need to spend the Theorem cost to enter a challenge again even after completing it previously.
You also retain the rewards from each EC without needing to purchase the EC studies again.
==Dilation Studies==
Main article: Time Dilation
Unlike other time studies, there are time studies that remains bought when you respec the time study tree. The first dilation study requires EC11x5 and EC12x5 to be completed instead. These time studies unlock new content including more Time Dimensions.