Liquidity Provision

LPs only deposit BT. For example:

• Initial deposit: 100 BT generates 100 vPT, forming the pool. LPs receive LP Shares.

• Redemption: LPs withdraw BT, and vPT is burned. If the vPT/BT ratio changes, the redemption logic adjusts accordingly.

Key Formulas:

• Total BT in pool: $BT_{tp}$

• Net BT: $BT_{net} = \text{Min}\left[{BT}_{tp}, {BT}_{tp} - ({PT}_c - {YT}_c)\right]$

• Net assets: $A_{net} = \text{Max}\left[{BT}_{tp}, {BT}_{tp} - ({PT}_c - {YT}_c)\right]$

Scenario 1:

When ${PT}_c \geq {YT}_c$

• LPs receive PT and LP Shares proportional to their BT deposit:

$$dPT = \frac{{PT}c - {YT}c}{A{net}} \times dBT, \quad dShare = \frac{{Share}{total}}{A_{net}} \times dBT$$

• Redemption yields BT and YT:

$$dBT = \frac{dShare \times {BT}{net}}{{Share}{total}}, \quad dYT = \frac{dShare \times ({PT}_c - {YT}c)}{{Share}{total}}$$

Scenario 2:

When ${PT}_c < {YT}_c$

• LPs receive YT and LP Shares:

$$dYT = \frac{{YT}c - {PT}c}{A{net}} \times dBT, \quad dShare = \frac{{Share}{total}}{A_{net}} \times dB$$

• Redemption yields BT and PT:

$$dBT = \frac{dShare \times {BT}{net}}{{Share}{total}}, \quad dPT = \frac{dShare \times ({YT}_c - {PT}c)}{{Share}{total}}$$

Proportionality Principle:

$$\text{Proportion} = \frac{{BT}{tp}}{vPT}, \quad \text{Proportion}_{\text{after}} = \text{Proportion}_{\text{before}}$$

Instant Mode

Instant Mode allows users to deposit BT to acquire LP shares without receiving PT or YT in return. Users who prefer simplified operations can opt for this mode. The underlying mechanism converts all PT or YT that the user would otherwise receive into BT, which is then injected into the liquidity pool. This process triggers a swap transaction for the user.