Dark Upgrades

Dark Upgrades (sometimes referred to as Darkness) are a set of upgrades unlocked after buying the 3^rd Aleph Upgrade. They cost Decrementy to upgrade, which is only attainable in Challenge 8.

Their costs are determined by $10^{\mathrm{log}_{10}(\mathrm{x})^{\mathrm{n}}}$ for $\mathrm{n}$ many times you've bought that Upgrade, where $\mathrm{x}$ represents the base Cost of the Dark Upgrade.

There are actually 9 Dark Upgrades in the game's code, but only 3 are shown.

Description	Base Cost	Scaling	Details
Reduce the potency of decrementy by 5%	1.00e5	^5	This simply raises the effect of Decrementy to the 0.95. The formula for this is $\mathrm{d}^{0.95^{\mathrm{u}}}$, where $\mathrm{d}$ represents the base effect of Decrementy, and $\mathrm{u}$ represents how many times you've bought this Upgrade.
Halve decrementy production under ωω3, otherwise double it	1.00e1000	^1000	The effect of this Upgrade might seem a bit misleading. Decrementy Growth Rate is actually square rooted ($\sqrt{x}$) if your Ordinal is below ωω3, otherwise it is then squared ($x^2$). The full, detailed formula is shown as $\mathrm{baseDecrementyGrowth}^{(2^{2*\mathrm{Ord}-1})^{\mathrm{darkUpgrade2}}}$, where $\mathrm{Ord}$ is 0 if your Ordinal is less than ωω3, or 1 otherwise; and $\mathrm{darkUpgrade2}$ represents how many times you've bought this Upgrade. This upgrade is boosted based on your OC2 completions.
Gain a 1.2x multiplier to Tier 1 and 2	1.00e9	^9	Useful for getting Challenge 8 completions and for speeding up the time to get to BHO. This multiplicatively stacks, just like all the other Upgrades.

There are also Dark Manifolds. They give a multiplier to only Dynamic Factor Cap. They start by costing 3 Decrementy and multiplies by 3 for every Dark Manifold you get, meaning that you can additively gain them.

The formula for the boost to Dynamic Factor cap given by Dark Manifolds is $(\mathrm{d}+1)^{0.1}$, where $\mathrm{d}$ is the number of Dark Manifolds you have.