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# $WALK (Utility Token) ####$WALK: Utility Token

$WALK is SuperWalk's utility token. • Token Name: Walk Token • Token Ticker:$WALK
• Total Issue: Unlimited
$WALK is issued unlimitedly, but it prevents excessive inflation by placing a daily total issue limit (Supply Cap). Users get scored through walking and running, measured by GPS and step sensors. Users receive a daily$WALK reward based on the points they had earned.
*WALK Distribution Time: 00:00 ~ 00:10 (UTC+9)

#### Problems with X2E

Paradoxically, the more popular the service is, the lower the price of utility tokens can be. Inflation of utility tokens occurs in the following situations:
• As the number of users increases, the issuance of utility tokens also increases rapidly. It causes hyperinflation of utility tokens, and therefore the value of the token declines.
• As the number of users increases, the number of NFTs increases, and the value of tokens decreases.
• As users increase their specifications, their payability increases. For example, if the performance indicators of shoe NFTs increase or the rate of energy and durability indicators wear down, users will be able to mine more tokens. It also contributes the decline in the value of the token.
The problem of the users leaving the game remains unresolved due to a large number of users who have experienced hyperinflation of utility tokens.
SuperWalk is running the project by introducing a token mechanism that can solve these problems from the following reasons.
*Key logic related to WALK will be updated regularly according to the project roadmap. We will transparently announce the data and decision-making process collected through the community prior to the major updates.

### 1. Point-based WALK Rewards

#### 1-1) Calculating the Point by user

SuperWalk's Shoes NFT users can earn points through GPS-based walking or running. The Point is determined by the following factors:
• GPS Accuracy
• Accuracy for target speed
• Energy consumed (exercise time)
• Types of Shoes NFT (walker, jogger, runner, all-rounder)
• Performance Stats for Shoes NFT
• Residual durability of Shoes NFT
• Probabilistic bonus point based on Luck stats in Shoes NFT
• Number of consecutive days of exercise (at least 5 minutes per day)
The equation of the point for each users after exercising for one minute is as follows.
$Point = Accuracy*(Parameter_t+Parameter_{p_1}*Parameter_{p_2})$
• Accuracy: Accuracy for target speed
• Parameter t: Variables related to the type of Shoes NFT
• Parameter p1: Variables associated with Performance Stat Figures in Shoes NFT
• Parameter p2: Variables related to durability
Based on Parameter t, weighting values are given depending on the type of shoes.

The Point Leaderboard allows users to view their points and the estimated amount of $WALK reward. This information is aggregated every hour and displayed on the leaderboard. The leaderboard will be intialized after distributing rewards every midnight KST(UTC+9) based on the point recieved. ### 2. Daily$WALK Reward Pool

The daily $WALK reward pool is scaled dynamically according to the logic phase setting variable. A key variable in the dynamic reward pool is the cost of repairs that entire user spends over a day. The main reason for setting the repair cost as a variable is that repair costs is the most obvious indicator of user activity. Furthermore, internal data showed that the correlation coefficient between repair cost, number of users, and the point was significant from 0.73 to 0.96. In addition, the daily$WALK Reward Pool will be divided into two parts to dissolve token acquisition polarization. Also, to guarantee the new entrants a minimum $WALK incinerated for the repair costs. 1. Base Reward Pool 2. Additional Reward Pool The description of these two pools follows: ### 3. Dynamic Emission Mechanism #### 3-1) Dynamic Emission Mechanism based on Repair Cost The daily$WALK reward pool is calculated according to the formula below. Variables for the Dynamic Emission Mechanism may vary by reflecting the accumulated CBT data. The variables that can be added later in the formula include:
• The number of Users (DAU, MAU)
• Repair Cost
• Total Cost (Costs for level-up, Repair cost, Minting cost)
• Net withdrawal of $WALK (Net selling amount) (1)$WALK Reward Pool
Below is the formula which decides the size of $WALK Reward Pool. $Pool_t=Pool_{t-1}*(RI_t+1)$ $Pool_t=Pool\ Size\ of\ time\ t$ $RI_t=Repair\ Index\ of\ time\ t$ The size of the$WALK reward pool and the Repair Index at time t are the major variables of the formula above.
$Base\ Pool_t=Pool_t*0.15$
$Additional\ Pool_t=Pool_t*0.85$
The daily $WALK reward pool will then be divided into the Base Reward Pool and the Additional Reward Pool at a rate of 15 to 85. Further details of the Base Reward Pool and the Additional Reward Pool will be described in depth below. *This rate may vary, depending on the Public Beta Test(PBT) data. (2)Repair Index Below is the formula of the Repair Index which is the major variable deciding the size of the$WALK Reward Pool.
$RI_t= \begin{cases} (if,\ a\geq0)\ \ \ min \begin{cases} a= {\Delta Parameter_{r_t}}*\beta \\ \\ b \end{cases} \\ \\ \\ (if,\ a<0)\ \ \ max \begin{cases} a={\Delta Parameter_{r_t}}*\beta \\ \\ -b \end{cases} \\ \end{cases}$
The major variable that decides the Repair Index is the change rate in the total repair cost at time t compared to time t-1.
For example, if the total Repair Cost at time t increased compared to time t-1, the calculated Repair Index will be positive. Substituting this Repair Index into the $WALK Reward Pool formula above, the$WALK Reward Pool size at time t will be greater than at time t-1.
In contrast, if the total Repair Cost at time t decreased compared to time t-1, the calculated Repair Index will be negative. Substituting this Repair Index into the $WALK Reward Pool formula above, the$WALK Reward Pool size at time t will be smaller than at time t-1.
In order to prevent rapid fluctuations of total repair costs between time t compared to time t-1, we set the maximum change rate of the Repair Index as b%. The number may vary, reflecting the accumulated test data.
The calculated daily $WALK Reward Pool will be allocated for the Base Reward Pool and the Additional Reward Pool at a rate of 15 to 85. (3) Base Reward Pool Over time, as the mining power of existing users strengthen, the mining power of new users will decrease dramatically. In order to minimize the gap of$WALK mining powers among those users, we decided to allocate a some part of the total $WALK Reward Pool for the Base Reward Pool. Below is the formula of the Base Reward Pool. $Base\ Reward_{Alice}=({\sqrt[3]{Point_{Alice}}\over\sum \sqrt[3]{Point_{user}}})*Base\ Pool_t$ (4)Additional Reward Pool The extra$WALK is distributed from Additional Reward Pool for the users with better attributes.
Below is the formula of the Additional Reward Pool.
$Additional\ Reward_{Alice}={Point_{Alice}\over \sum (Point_{user})}*Additional\ Pool_t$

### Dynamic Reward v2

(5) V1 Reward
Until the additional reward pool, the existing dynamic reward remains the same, but there is now a newly added feature called dynamic reward v2. The v1 reward is calculated by adding the base reward and the additional reward.
$V1\ Reward_{Alice}=Base_{Alice}+Additional_{Alice}$
Then, the v1.5 reward is calculated by taking the minimum value between the v1 reward and the points earned by the user on that day.
$V1.5\ Reward=min(V1\ Reward,\ Point)$
As a result, users who previously received more distribution than points will now receive WALK distribution at a 1:1 ratio with their points.
(6) V2 Reward
$V2\ Reward=V1.5\ Reward+\alpha$
Users who meet certain conditions will receive an additional reward of "a," and the sum of "a" and the v1.5 reward will become the v2 reward.
$\Sigma\ \alpha =Surplus Reward = Pool\ Size-\Sigma V1.5\ Reward$
The condition reward "a" is the difference between the pool size and the total v1.5 reward. The v1.5 reward is always less than or equal to the v1 reward, and if the v1.5 reward is less than the v1 reward, only a smaller number than the pool size will be distributed. Therefore, any unallocated reward will become the "a" reward.
(7) Distribution of "a"(Condition Reward)
We plan to study various condition reward distribution criteria in the future. Initially, we will distribute condition rewards based on the points familiar to existing users. Users whose rank on the distribution date is in the top x% will receive differentiated condition rewards according to the following formula. The condition reward will be calculated based on the weight of the points obtained by each user.
(The distribution criteria and number of recipients in this whitepaper are subject to change at any time for testing and optimization of the new system.)
Users whose rank on the distribution date is in the top x% will receive differentiated condition rewards based on the following formula.
$WP_{Alice}(weighted\ point)={Point_{Alice}\over \Sigma^n_{rank=1}Point_{user}}$
$if)\ Alice's\ Rank>n,\ \ WP_{Alice}=0$
$\alpha_{Alice}=WP_{Alice}*Surplus\ Reward$
$V2\ Reward_{Alice}=V1.5\ Reward_{Alice}+\alpha_{Alice}$
🔑 Examples of calculating the $WALK Reward Pool The following two examples shows the$WALK Reward Pool is decided by using the change rate in the total repair cost between two different times.
*This example will help users to undestand calculation of the $WALK reward pool. The numbers can differ from the actual logic. e.g.1) Case of decreased$WALK Reward Pool on Day 2 compared to Day 1, the amount of $WALK that John may receive will be as follows:$WALK Reward Pool size of Day 1: 100,000 $WALK Repair Cost of Day 1: 70,000$WALK
Repair Cost of Day 2: 68,000 $WALK The change rate of Repair Cost on Day 1 compared to Day 2: -2.857%$WALK Reward Pool size of Day 2: 97,143 $WALK If John’s point on Day 2 is 300, he gets 291.43$WALK at midnight, according to the distribution logic.
e.g.2) Case of increased $WALK Reward Pool on Day 2 compared to Day 1, the amount of$WALK that John may receive will be as follows:
$WALK Reward Pool size of Day 1: 100,000$WALK
Repair Cost of Day 1: 70,000 $WALK Repair Cost of Day 2: 72,000$WALK
The change rate of Repair Cost on Day 1 compared to Day 2: +2.857%
$WALK Reward Pool size of Day 2: 102,857$WALK
Dynamic reward v1: If John’s point on Day 2 is 300, he gets 308.57 \$WALK at midnight, according to the distribution logic.
Dynamic reward v2: If John's points on the second day are 300 points, according to the distribution logic at midnight on the second day, he would be calculated to receive 308.57 WALK tokens. However, according to the new logic added in v2, he will receive the minimum value between his points and the settlement value, which is 300 WALK tokens. If John becomes eligible for a condition reward, he will receive additional surplus rewards according to the condition reward distribution logic.