# 🔍Mathematical Model

**Guide**:

$TOKENi$: Amount of BRC20 tokens received by user $i$.

$Ci$: Commitment of dKOI by user $i$.

$Ctotal$: Total commitment of dKOI from all users.

$G$: Fundraising goal in dKOI.

$P$: Percentage of dKOI used for TOKEN purchase.

$R$: Oversubscription ratio ($Ctotal/G$).

**Proportional Allocation Model:**

The formula for calculating the amount of BRC20 tokens ($TOKENi$) received by user $i$ is:

#### Refund Model:

The formula for the refund amount ($Refundi$) for each user is:

**Final KOI Model:**

The final amount of dKOI that a user would receive ($FinalKOI$i) is:

The Proportional Allocation Model (PAM) ensures a proportional distribution of the BRC20 tokens among users based on their individual commitments relative to the total commitment.

In the case of oversubscription, where the total commitment exceeds the fundraising goal, the allocation is capped at the minimum of the total commitment and the goal. Additionally, users receive a refund proportional to their commitment beyond the fundraising goal, with the overall goal of maintaining fairness and proportionality in the distribution of tokens and refunds among participating users.

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