Imaginary Upgrades

Once you are able to gain at least 1e1000 Reality Machines in a single Reality (requires 2.15e1337333 EP), you unlock the ability to gain a new resource called Imaginary Machines. Reality Machines will also become hardcapped at 1e1000; you'll be unable to gain any more past this limit.
Additionally you unlock the Imaginary Upgrades tab, which contains a set of upgrades similar to the Reality Upgrades - each upgrade has a condition you must fulfill to unlock it and an Imaginary Machine cost to actually purchase it. The first two rows of upgrades can be repeatedly bought, while the other three are one-time upgrades.
Your iM amount is affected by two things:
iM Cap - There is a maximum amount of iM you can ever have, which is based on the highest RM amount you would have been able to get if there were no RM cap (based on your highest EP). This is updated on a continual basis and thus will immediately increase if you ever surpass your previous highest uncapped RM amount.
The iM Cap formula is: {(log(RM)-1000)}^{2}\max({(log(RM)-100000)}^{0.2},1)
Imaginary Machines are gained passively over time up to the cap, but gain slows down exponentially as you approach the cap.
By default, for every 60 seconds, the difference in iM between your current amount and the cap will be cut in half.
For example: If you have 1e7 iM and the cap is 9e7 iM (difference: 8e7), the next minute will have 5e7 iM (difference: 4e7 (8e7/2)), then another minutes you will have 7e7 iM (difference: 2e7 (8e7/2^2)), 3 minutes later you will have 8e7 iM (difference: 1e7 (8e7/2^3)), you will have 8.5e7 iM after 4 minutes (difference: 5e6 (8e7/2^4))
Another example: If you have 1e10 iM and the cap is 1.1e11 (1e11 to cap), the next second will have 1.11e10 iM (9.89e10 (1e11/2^(1/60)) to cap), after 5 seconds, you will have 1.56e10 iM (9.44e10 (1e11/2^(1/12)) to cap), in 10 seconds you will have 2.09e10 iM (8.91e10 (1e11/2^(1/6)) to cap), you will have 3.93e10 iM after 30 seconds (7.07e10 (1e11/2^(1/2)) to cap)
iM Cap	Required Highest EP	iM Cap 	Required Highest EP
0 	2.15e1,337,333 	100 	4.64e1,350,666
1 	4.64e1,338,666 	1,000 	1.09e1,379,497
2 	8.94e1,339,218 	10,000 	4.64e1,470,666
3 	5.43e1,339,642 	100,000 	2.26e1,758,970
4 	1e1,340,000 	1,000,000 	4.64e2,670,666
5 	5.72e1,340,314 	10,000,000 	3.52e5,553,703
6 	2.09e1,340,599 	100,000,000 	4.64e14,670,666
7 	1e1,340,861 	1,000,000,000 	2.94e43,501,035
8 	3.71e1,341,104 	10,000,000,000 	2.96e133,338,807
9 	2.15e1,341,333 	100,000,000,000 	1.88e158,724,918
10 	5.05e1,341,549 	1,000,000,000,000	2.94e395,421,141
Current iM - Over time your current iM will passively rise towards your iM cap, in a way that slows down exponentially as you approach the cap. By default iM slows down at a rate where the amount you are missing (ie. your cap minus your current amount) is cut in half every minute. This growth rate is unaffected by any modifiers to game speed.
Imaginary Machine upgrades will unlock the final two Celestials.
==Repeatable Upgrades==
Name 	Effect 	Base Cost (iM)	Cost Scaling
Temporal Intensifier 	Increase Temporal Amplifier multiplier by +0.15 per level 	3 	60
Replicative Intensifier 	Increase Replicative Amplifier multiplier by +0.15 per level 	4 	60
Eternal Intensifier 	Increase Eternal Amplifier multiplier by +0.4 per level 	1 	40
Superluminal Intensifier	Increase Superluminal Amplifier multiplier by +0.15 per level	5 	80
Boundless Intensifier 	Increase Boundless Amplifier multiplier by +0.6 per level 	1 	30
Elliptic Materiality 	Increase the Reality Machine cap by x1e100 per level 	10,000 	500
Runic Assurance 	Delay Glyph Instability starting level by 200 per level 	200,000 	500
Hyperbolic Apeirogon 	Multiply Infinity Dimensions by 1e100,000 per level 	10,000,000 	800
Cosmic Filament 	Increase Galaxy strength by +3% per level 	1,000,000,000 	1,000
Entropic Condensing 	Increase Singularity gain by +100% per level 	8,000,000,000 	2,000
==Non-Repeatable upgrades==
In addition to costing imaginary machines, non-repeatable upgrades have an unlock condition. 
Name 	Effect 	Unlock Condition 	Details 	Cost (iM)	Required Highest EP
Suspicion of Interference	Time Dimension power based on total antimatter 	1e90 total Relic Shards 	^(1+log(log(total AM))/100) 	5e7 	
Consequences of Illusions	Gain free Dimboosts based on Imaginary rebuyable count 	Make a level 9000 Glyph with a single Glyph level factor weight at 100 	+20,000 per Imaginary rebuyable level 	5e7 	
Transience of Information	Increase Imaginary Machine Cap based on Imaginary Upgrades purchased 	Reach 1.80e308 projected Reality Machines within The Nameless Ones' Reality 	1, +0.05 per Imaginary rebuyable level, and +0.5 per one-time Imaginary upgrade.	5e7 	
Recollection of Intrusion	Raise all Dimension per-purchase multipliers to ^1.5 	Reach a tickspeed of e7.5e10 / sec within Eternity Challenge 5 	 	3.5e8 	
Fabrication of Ideals 	Convert Antimatter Dimensions to Continuum and unlock Lai'tela, Celestial of Dimensions 	Reach e1.5e12 antimatter without ever having any 1st Infinity Dimensions 	Continuum replaces your Antimatter Dimension and Tickspeed Autobuyers, as your production multipliers
now automatically and continuously scale based on how many purchases you would have had otherwise.	1e9 	2.94e43,501,035
Massless Momentum 	Unlock the 2nd Dark Matter Dimension 	Destabilize Lai'tela's Reality in under 30 seconds twice 	 	3.5e9 	
Chiral Oscillation 	Unlock the 3rd Dark Matter Dimension 	Automatically condense at least 20 Singularities at once 	 	6e9 	
Dimensional Symmetry 	Unlock the 4th Dark Matter Dimension 	Have 80,000 total Galaxies 	 	1.5e10 	
Deterministic Radiation 	Unlock Dark Matter Annihilation 	Reach 3,850,000 Tickspeed Continuum without ever having more than 8 Time Studies in this Reality 	 	2.8e10 	
Vacuum Acceleration 	Unlock Autobuyers for repeatable Imaginary Upgrades and generate Imaginary Machines 10 times faster	Have a Continuum increase of at least 100% 	 	3e12 	
Existential Elimination 	Annihilation multiplier gain is improved based on Imaginary Machines 	Reach e7.4e12 antimatter with Continuum disabled 	(log(iM)-10)^3, minimum at 1 (1e11 iM) 	1e13 	
Total Termination 	Glyph Sacrifice totals for all Glyphs are increased to 1e100 	Reach e1.5e11 antimatter in Effarig's Reality with at least 4 Cursed Glyphs equipped 	 	1.5e14 	
Planar Purification 	Increase free Dimboost count based on Tesseract count 	Reach Glyph level 20000 in Ra's Reality with at most 0 Glyphs equipped 	Effective Tesseract^2/4, round down, multiplicative 	6e14 	
Absolute Annulment 	Increase free Dimboost strength based on Singularity count 	Have 13000 Antimatter Galaxies in Ra's Reality with a fully inverted Black Hole 	Singularities^300 	6e14 	
Omnipresent Obliteration 	Unlock Pelle, Celestial of Antimatter 	Reach Reality in Lai'tela's Reality with all Dimensions disabled and at least 4 empty Glyph slots	 	1.6e15