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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
RA×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.
Fig. 5. A visualization of the 3D CPF.
Definition 3. For a pool of
AA
,
BB
, and compulsory
SENSEN
, the 3D constant product function is:
(33)
RA×RB×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
RA×RB=kRSEN=kR_A\times{R_B}=\frac{k}{R_{SEN}}=k'
​, where
kk'
is a constant as well.
Assume a trader swaps
rAr_A
for
rBr_B
, the newest state of token
AA
would be
RA=RA+rAR'_A=R_A+r_A
​. Because of the CPF, we have:
(34)
RB=RARBRA=RARBRA+rAR'_B=\frac{R_AR_B}{R'_A}=\frac{R_AR_B}{R_A+r_A}
.