The Triad Pool

Swap any and every pairs. Never think about how you should divide your portfolio ever again.

Recall that the most well-adopted CPF is two-dimensional where RAΓ—RB=kR_A\times{R_B}=k. In Sentre, however, the pool can be optionally organized into three tokens. It’s now the pool of triad and the CPF turns to three-dimensional where the third dimension is for SENSEN as in Fig. 5.

Definition 3. For a pool of AA, BB, and compulsory SENSEN, the 3D constant product function is:

(33) RAΓ—RBΓ—RSEN=kR_A\times{R_B}\times{R_{SEN}}=k​,

where kk is a constant.

To deposit to the pool, a liquidity provider (LP) theoretically needs to divide their portfolio into three equal portions regarding value. However, LPs never worry about this due to Simulated Single Exposure which allows people to deposit even on one side (see Asymmetric Deposit). Especially, although the formula has a higher dimension, the formula isn’t much different from the 2D CPF in trading.

When a trader swaps AA from BB, for example, the third token, which is SENSEN​ in this case, will be ignored. The formula is boiled down to RAΓ—RB=kRSEN=kβ€²R_A\times{R_B}=\frac{k}{R_{SEN}}=k'​, where kβ€²k' is a constant as well.

Assume a trader swaps rAr_A for rBr_B, the newest state of token AA would be RAβ€²=RA+rAR'_A=R_A+r_A​. Because of the CPF, we have:

(34) RBβ€²=RARBRAβ€²=RARBRA+rAR'_B=\frac{R_AR_B}{R'_A}=\frac{R_AR_B}{R_A+r_A}.

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