# Sliding Emissions Theory

In order to build a sustainable passive emissions model, an *Emissions Ratio* will be applied to the actual emissions all Gacha Girls will receive. Specifically, the amount of $ARC tokens that any Gacha Girl receives based on her *Emission Value* will be determined by this *Emissions Ratio*. The Emissions Ratio will be determined by accounting for the current amount of $ARC tokens left to be passively emitted to Gacha Girls compared to the original amount of $ARC tokens designated for passive emission.

First, let’s put it in simple terms:

IF there are exactly 34.710.000 $ARC tokens or more left to be passively emitted to Gacha Girls (69.420% of the total $ARC supply), every Gacha Girl will receive daily $ARC tokens equal to her Emission Value (Base Emission Value multiplied by the Emission Multiplier). For example, a Gacha Girl with Gamer Score 8 and Cosmic Tier 2 has an Emission Value of 6.25, and will thus receive 6.25 $ARC tokens daily.

IF there are

*less*than 34.710.000 $ARC tokens left to be passively emitted to Gacha Girls, every Gacha Girl will receive daily $ARC tokens equal to her Emission Value multiplied by the Emissions Ratio.

The Emissions ratio is calculated first obtaining the ratio of current $ARC tokens left to be passively emitted to Gacha Girls compared to the original amount of $ARC tokens designated for passive emission. For example, if there are 27.768.000 $ARC tokens left to be passively emitted to Gacha Girls, the ratio compared to the original amount of $ARC tokens designated for passive emission is 80%.

Next, we inject the previously obtained ratio (Passive_P2E_Ratio) into the following formula:

*Emissions Ratio* = 839123.4 + (0.02104839 – 839123.4)/(1 + ( Passive_P2E_*Ratio* /1764.034)^1.828774)

To reiterate, this Emissions Ratio will only be applied if there are *less* $ARC tokens left to be passively emitted to Gacha Girls compared to the original amount of $ARC tokens designated for passive emission (i.e., 69.420% of the total supply). This Emissions Ratio will help ensure that our passive emissions system is more sustainable than more basic or flat distribution models.

To help conceptualize this, you can look at this example of how the Passive_P2E_Ratio affects the actual emissions for a Gacha Girl with maximum upgrades.
**TLDR; You get more overall $ARC if you upgrade your girls early!**

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