Adaptive-Rate-Limiters

Implemented to curtail the effects of hyper-compounding and foster long-term viability.

GalaxyCash has introduced Adaptive Rate Limiters to mitigate the impacts of excessive compounding and enhance sustainability.

There are 5 tiers of Rate Limiters, and your tier is determined by the ratio of your compounded rewards to your fresh gFrax deposits.

This can be calculated using the following formula:

Define the Compound Reward Function (C(n)) and the New Deposit Function (D(m)), where (n) and (m) denote the number of days. For a specific time period (t), the total compounded rewards and new deposits are given by:

$$Ctotal(t)=\sum_{i=1}^{t} C(i), Dtotal(t)=\sum_{j=1}^{t} D(j)$$

The level of Adaptive-Rate-Limiters (L) is determined using this conditional function:

$$L(x) = \begin{cases} 0.0045 & \text{if } 50,000 \leq x < 250,000 \\ 0.00425 & \text{if } 250,000 \leq x < 500,000 \\ 0.00375 & \text{if } 500,000 \leq x < 750,000 \\ 0.00325 & \text{if } 750,000 \leq x < 1,000,000 \\ 0.0025 & \text{if } x \geq 1,000,000 \end{cases}$$

Here, (x) is the value of the Rate Limiter, derived from the difference between compounded rewards and new deposits:

$$x=Ctotal(t)−Dtotal(t)$$

The daily earnings (E) on any given day (k) are the current balance (B(k)) multiplied by the corresponding rate (L(x)):

$$E(k)=B(k)⋅L(x)$$

The balance update (B) is a recursive function, where (B(0)) is the initial balance:

$$B(k+1)=B(k)+E(k)$$

This recursive relationship allows for calculating the balance for any future day, based on the previous day's balance and the earnings of that day. The continuous growth of future balances can be modeled using the Laplace transform of L:

$${L}\{ B(t) \} = \mathcal{L}\{ B(0) \} + \mathcal{L}\{ \sum_{k=0}^{t-1} E(k)$$

The limiters are as follows:

1. 50,000 to 249,999 Daily rate 0.45%

2. 250,000 to 499,999 Daily rate 0.425%

3. 500,000 to 749,999 Daily rate 0.375%

4. 750,000 to 999,999 Daily rate 0.325%

5. 1,000,000 and above Daily rate 0.25%

Example

Total Compounded Rewards = 600,000 gFrax New Deposit = 25,000 gFrax

600,000 - 25,000 = 575,000 gFrax (Tier 3 applied, Daily Rate 0.375%)