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# vooi Pool

vooi Pool Math

The vooi pool is an AMM liquidity pool that contains tokens of the same face value. Any token can be swapped for any other available token within the pool, ensuring that there are no restrictions on token pairs.

The vooi pool permits single-side token provisioning. This strategy not only simplifies the process for liquidity providers but also optimizes user experience.

The vooi pool has robust mechanisms in place that ensure maximum capital utilization. More impressively, it achieves this without subjecting its users to the typical impermanent losses due to price movements.

Each token in the pool is associated with two concepts: asset and liability, wherein:

- 1.The asset of token$k$represents the amount of that token available for operations (withdrawal or exchange) at a given moment.
- 2.The liability of token$k$indicates how much the pool "owes" its liquidity providers at that moment.

When the asset of each token is equal to its liability in the pool, then the pool is in an equilibrium state. The pool always tries to reach this state of equilibrium.

The coverage ratio for each token is calculated as follows:

$r_k=A_k/L_k$

, where $A_k$

is the asset of token $k$

available for operating (withdrawal or exchange), and $L_k$

is the liability of token $k$

.So using the coverage ratio the equilibrium state can be defined as:

$r_k=1$

for any $k\subseteq T,$

where $T$

is the set of all tokens in the pool.At the core of any Automated Market Maker (AMM) protocol is a fundamental mathematical relationship known as an invariant curve. This curve serves as a crucial link between the coverage ratios of the various tokens that make up the liquidity pool. The concept underlying this structure is that regardless of the specific transactions taking place within the pool — be it token swaps, withdrawals, or additions of liquidity — the equilibrium of coverage ratios must consistently conform to the conditions set forth by this invariant curve equation. In essence, this equation acts as a governing principle, ensuring the integrity and stability of the AMM system by maintaining a harmonious balance among the different tokens in the pool.

Here is an invariant curve for the vooi pool:

$\sum_{k\subseteq T}{L_k(r_k - \frac{A}{r_k})}=const$

, where $T$

is the set of the all token types in the pool, $L_k$

is the liability of token $k$

, $r_k$

is the coverage ratio of token $k$

, and $A$

is the amplification coefficient, which is in between 0 and 1. This default parameter scales the entire price range.vooi pool contract address on the Linea network:

`0xBc7f67fA9C72f9fcCf917cBCEe2a50dEb031462A`

Last modified 6mo ago