How JetPack Tokens Work

The JetPack token system comprises activity-based token issuance and distribution, a service level system, user rewards and token utilization methods, and a mechanism for purchasing and redistributing tokens. This structure provides a fair and efficient reward system for both users and service providers.

Token Distribution (Drop) Mechanism

Total Token Supply and Distribution Period

• Total Supply: JetPack will issue a total of 1 billion Jet tokens.
• Distribution Period: Tokens will be distributed over 38 years, with a total of 2,776 distributions occurring at the same intervals as the Cardano Epoch (1 epoch = 5 days).

Token Distribution Amount per Epoch

Calculating Distribution Amount Based on a Logarithmic Function

The amount of tokens distributed per epoch is designed to decrease over time. A logarithmic function is used to calculate the distribution amount for each epoch. 1 Jet equals 1,000,000 Pack, so the distribution amounts are calculated to the sixth decimal place and paid accordingly.

1. Definition of the Logarithmic Function $f(t)$:

   $$f(t) = \dfrac{1}{\ln(t + 1)}$$

   Where:

   • $t$ is the epoch number, $t = 1, 2, 3, \dotsc, 2776$.
   • $\ln$ is the natural logarithm function.

2. Calculating the Sum of the Log Function $f(t)$ Over All Epochs:

   The total sum of the function values over the entire distribution period $S$ is:

   $$S = \sum_{t=1}^{2776} f(t) = \sum_{t=1}^{2776} \dfrac{1}{\ln(t + 1)}$$

3. Calculating the Scaling Constant $A$:

   The total token supply of 1 billion Jet is divided by the sum $S$ to adjust the distribution amount for each epoch:

   $$A = \dfrac{1,000,000,000}{S} = 2,412,005.7263929145$$

4. Calculating the Token Distribution Amount per Epoch:

   The distribution amount for each epoch is:

   $$\text{Distribution Amount}_t = A \times f(t) = A \times \dfrac{1}{\ln(t + 1)}$$

5. Examples of Distribution Amounts:

   Calculating the distribution amounts for the initial epochs:

   • Epoch 1:

     $$\text{Distribution Amount}_1 = 3,479,788.70 = A \times \dfrac{1}{\ln(1 + 1)} = A \times \dfrac{1}{\ln(2)}$$

   • Epoch 2:

     $$\text{Distribution Amount}_2 = 2,195,502.227 = A \times \dfrac{1}{\ln(2 + 1)} = A \times \dfrac{1}{\ln(3)}$$

   • Epoch 3:

     $$\text{Distribution Amount}_3 = 1,739,894.35 = A \times \dfrac{1}{\ln(3 + 1)} = A \times \dfrac{1}{\ln(4)}$$

   The distribution amount for each epoch is determined by the value of the log function corresponding to the epoch number.

Distribution Characteristics

• Since $\ln(t + 1)$ increases as $t$ increases, the denominator becomes larger, causing the overall distribution amount to gradually decrease.
• The distribution amount per epoch decreases over time, approaching zero.
• This design incentivizes early participants and increases the scarcity of the token.

Overall Distribution Schedule

Below is a partial table summarizing the distribution amounts and dates per epoch. For detailed information on all epochs, please refer to the separate document and code.

Token Distribution Criteria per Service

Calculating Ratios Among Services

The distribution ratio for each service is calculated based on its performance score $P_n$ relative to the total performance score $P$:

Where:

• $P_n$: Performance score of service $n$.
• $P$: Sum of performance scores of all services.

Calculating Distribution Amount per Service

The amount of tokens that service $n$ receives in each epoch $S_n$ is:

• $f_{\text{total}}(t)$: Adjusted total distribution amount for the epoch.
• $\text{Maximum Token Distribution for Service } n$: Maximum token amount allocated based on the service’s level (see level-based maximum token distribution below).

Handling of Undistributed Tokens

Carrying Over Undistributed Tokens

• Undistributed tokens from each epoch are added to the total distribution amount for the next epoch.
• This ensures effective token distribution even when initial service participation is low.

Calculating Adjusted Total Distribution Amount per Epoch

The total distribution amount for the next epoch is:

• $f_{\text{total}}(t+1)$: Adjusted total distribution amount for epoch $t+1$.
• $A \times f(t+1)$: Distribution amount based on the basic distribution function.
• Carried-over Undistributed Tokens: Number of tokens not distributed in epoch $t$.

Calculating Performance Score ($P_n$) per Service

Each service’s performance score is calculated based on the following metrics. The weight of each metric can be adjusted through governance.

1. JetPack Token Consumption ($M_{1n}$)

   • Weight: $w_1 = 50\%$
   • Description: Total amount of JetPack tokens consumed by users within the service.

2. Degen Bunny Vote Count ($M_{2n}$)

   • Weight: $w_2 = 30\%$
   • Description: Number of votes received from OG Degen Bunnies.

3. Active User Count ($M_{3n}$)

   • Weight: $w_3 = 20\%$
   • Description: Number of unique users who accessed and were active in the service during the epoch.

Each service’s performance score $P_n$ is calculated as:

Where:

• $M_{1n}$: JetPack token consumption of service $n$.
• $M_{1\text{total}}$: Total JetPack token consumption across all services.
• $M_{2n}$: Degen Bunny vote count for service $n$.
• $M_{2\text{total}}$: Total Degen Bunny votes across all services.
• $M_{3n}$: Active user count of service $n$.
• $M_{3\text{total}}$: Total active users across all services.

Example:

• Service A:
  • $M_{1A} = 500$
  • $M_{2A} = 150$
  • $M_{3A} = 200$
• Service B:
  • $M_{1B} = 300$
  • $M_{2B} = 200$
  • $M_{3B} = 100$
• Service C:
  • $M_{1C} = 200$
  • $M_{2C} = 150$
  • $M_{3C} = 700$

Totals:

• $M_{1\text{total}} = 500 + 300 + 200 = 1000$
• $M_{2\text{total}} = 150 + 200 + 150 = 500$
• $M_{3\text{total}} = 200 + 100 + 700 = 1000$

Weights:

• $w_1 = 0.5$
• $w_2 = 0.3$
• $w_3 = 0.2$

Calculating Performance Score for Service A:

Calculating Performance Score for Service B:

Calculating Performance Score for Service C:

Thus, the performance scores are:

• Service A: $P_A = 0.38$
• Service B: $P_B = 0.29$
• Service C: $P_C = 0.33$

Level Determination Criteria and Maximum Token Distribution Amount

Based on the performance score $P_n$, each service is classified into Levels 1 through 9. This classification uses the cumulative top percentile of all services’ performance scores.

Cumulative Top Percentiles and Maximum Token Distribution Amounts per Level

Level Determination Method

1. Calculate Performance Scores

   Use the previously defined method to calculate each service’s performance score $P_n$.

2. Determine Service Rankings

   Rank all services in descending order based on their performance scores.

3. Calculate Cumulative Top Percentiles

   For each service, calculate the cumulative top percentile:

   $$\text{Cumulative Top Percentile (\%)} = \left(1 - \frac{\text{Rank} - 1}{N} \right) \times 100\%$$

   Where:

   • $\text{Rank}$: The service’s rank (starting from 1).
   • $N$: Total number of services.

4. Assign Levels

   Assign levels based on the cumulative top percentiles:

   • Level 1: Cumulative top percentile > 96%
   • Level 2: 89% < Cumulative top percentile ≤ 96%
   • Level 3: 77% < Cumulative top percentile ≤ 89%
   • Level 4: 60% < Cumulative top percentile ≤ 77%
   • Level 5: 40% < Cumulative top percentile ≤ 60%
   • Level 6: 23% < Cumulative top percentile ≤ 40%
   • Level 7: 11% < Cumulative top percentile ≤ 23%
   • Level 8: 4% < Cumulative top percentile ≤ 11%
   • Level 9: Cumulative top percentile ≤ 4%

Example:

With a total of 3 services:

1. Calculate Rankings and Cumulative Top Percentiles

   • Service A:

     • Performance Score: $P_A = 0.38$

     • Rank: 1

     • Cumulative Top Percentile:

       $$\text{Cumulative Top Percentile} = \left(1 - \frac{1 - 1}{3} \right) \times 100\% = 100\%$$

   • Service C:

     • Performance Score: $P_C = 0.33$

     • Rank: 2

     • Cumulative Top Percentile:

       $$\text{Cumulative Top Percentile} = \left(1 - \frac{2 - 1}{3} \right) \times 100\% = 66.67\%$$

   • Service B:

     • Performance Score: $P_B = 0.29$

     • Rank: 3

     • Cumulative Top Percentile:

       $$\text{Cumulative Top Percentile} = \left(1 - \frac{3 - 1}{3} \right) \times 100\% = 33.33\%$$

2. Assign Levels

   • Service A:

     • Cumulative Top Percentile: 100%
     • Level: Level 1 (Cumulative Top Percentile > 96%)
     • Maximum Token Distribution: 30,000 Jet

   • Service C:

     • Cumulative Top Percentile: 66.67%
     • Level: Level 4 (60% < Cumulative Top Percentile ≤ 77%)
     • Maximum Token Distribution: 15,000 Jet

   • Service B:

     • Cumulative Top Percentile: 33.33%
     • Level: Level 6 (23% < Cumulative Top Percentile ≤ 40%)
     • Maximum Token Distribution: 7,000 Jet

Notes:

• Tied Scores: Services with identical performance scores receive the same rank. In calculating cumulative top percentiles, the average rank is used.
• Maximum Token Distribution refers to the maximum token amount a service can receive based on its level.

Example Scenario

Epoch 1 ($t = 1$)

• Basic Distribution Amount: $f(1) = 3,479,788.70 \text{ Jet}$
• Adjusted Total Distribution Amount: $f_{\text{total}}(1) = 3,479,788.70 \text{ Jet}$

Calculating Distribution Amount per Service

Based on the performance scores and levels:

• Total Performance Score $P$: $P = P_A + P_B + P_C = 0.38 + 0.29 + 0.33 = 1.00$

1. Service A:

   • Ratio: $\frac{P_A}{P} = \frac{0.38}{1.00} = 0.38$

   • Distribution Amount:

     $$S_A = \min\left( 3,479,788.70 \times 0.38, 30,000 \right) = \min(1,322,319.71, 30,000) = 30,000 \text{ Jet}$$

2. Service C:

   • Ratio: $\frac{P_C}{P} = \frac{0.33}{1.00} = 0.33$

   • Distribution Amount:

     $$S_C = \min\left( 3,479,788.70 \times 0.33, 15,000 \right) = \min(1,148,330.27, 15,000) = 15,000 \text{ Jet}$$

3. Service B:

   • Ratio: $\frac{P_B}{P} = \frac{0.29}{1.00} = 0.29$

   • Distribution Amount:

     $$S_B = \min\left( 3,479,788.70 \times 0.29, 7,000 \right) = \min(1,009,138.72, 7,000) = 7,000 \text{ Jet}$$

Distribution Results

• Total Tokens Distributed: $30,000 + 15,000 + 7,000 = 52,000 \text{ Jet}$
• Undistributed Tokens: $3,479,788.70 - 52,000 = 3,427,788.70 \text{ Jet}$

Epoch 2 ($t = 2$)

• Basic Distribution Amount:

  $$f(2) = 2,195,502.227 \text{ Jet}$$

• Carried-over Tokens: $3,427,788.70 \text{ Jet}$

• Adjusted Total Distribution Amount:

  $$f_{\text{total}}(2) = 2,195,502.227 + 3,427,788.70 = 5,623,290.927 \text{ Jet}$$

Updated Performance Scores and Levels

Assuming changes in performance scores:

• Service A:

  • Performance Score: $P_A = 0.40$
  • Rank: 1
  • Cumulative Top Percentile: 100%
  • Level: Level 1
  • Maximum Token Distribution: 30,000 Jet

• Service C:

  • Performance Score: $P_C = 0.35$
  • Rank: 2
  • Cumulative Top Percentile: 66.67%
  • Level: Level 4
  • Maximum Token Distribution: 15,000 Jet

• Service B:

  • Performance Score: $P_B = 0.25$
  • Rank: 3
  • Cumulative Top Percentile: 33.33%
  • Level: Level 6
  • Maximum Token Distribution: 7,000 Jet

Total Performance Score $P$: $P = 0.40 + 0.35 + 0.25 = 1.00$

Calculating Distribution Amount per Service

1. Service A:

   • Ratio: $\frac{P_A}{P} = 0.40$

   • Distribution Amount:

     $$S_A = \min\left( 5,623,290.927 \times 0.40, 30,000 \right) = \min(2,249,316.37, 30,000) = 30,000 \text{ Jet}$$

2. Service C:

   • Ratio: $\frac{P_C}{P} = 0.35$

   • Distribution Amount:

     $$S_C = \min\left( 5,623,290.927 \times 0.35, 15,000 \right) = \min(1,968,151.83, 15,000) = 15,000 \text{ Jet}$$

3. Service B:

   • Ratio: $\frac{P_B}{P} = 0.25$

   • Distribution Amount:

     $$S_B = \min\left( 5,623,290.927 \times 0.25, 7,000 \right) = \min(1,405,822.73, 7,000) = 7,000 \text{ Jet}$$

Distribution Results

• Total Tokens Distributed: $30,000 + 15,000 + 7,000 = 52,000 \text{ Jet}$
• Undistributed Tokens: $5,623,290.927 - 52,000 = 5,571,290.927 \text{ Jet}$

Impact of Accumulated Undistributed Tokens

• Increased Service Participation and Improved Performance will gradually reduce the amount of undistributed tokens.
• Initial services can utilize the maximum distribution amount to foster growth.
• Carrying over tokens helps maintain value stability and regulate circulation.

User Rewards and Token Usage

User Reward Mechanism

• Activity-Based Rewards: Users receive JetPack tokens when they perform pre-agreed activities (e.g., content creation, gameplay) within a service.
• Token Reward Criteria: The amount of tokens rewarded for each activity is determined through consultation between the service and the JetPack ecosystem operator.

Token Usage Methods

1. Within the Service:

   • Access Premium Features: Use tokens to access paid features or content within the service.
   • Purchase Goods: Buy digital goods or in-service items using tokens.

2. Using the JetPack Wallet Service Exchange:

   • Token Sales: Users can exchange their tokens for ADA (the currency of Cardano).
   • Wallet Management: The JetPack wallet allows secure management of tokens and transfers to other services.

Expected Benefits from Token Value Appreciation

• Token Liquidity: Trading tokens on exchanges increases their liquidity.
• Economic Gains: Users can achieve additional economic benefits by selling tokens if their value appreciates.

Token Purchase and Redistribution

Additional Token Purchases by Services

• When Distributed Tokens Are Depleted: If a service uses all its allocated tokens, it can purchase additional tokens from the JetPack Wallet Service Exchange.
• Purchase Currency: Tokens are purchased using ADA.
• Utilization of Purchased Tokens: Purchased tokens can be used to reward users or within the service.

Resellable vs. Non-Resellable Tokens

• Distributed Tokens (Non-Resellable): Tokens allocated to services cannot be resold and are only for user rewards.
• Purchased Tokens and Tokens Acquired from Users (Resellable): Tokens bought with ADA and tokens received from users can be resold, aiding in liquidity acquisition.

Token Redistribution and Ecosystem Activation

1. Token Circulation Structure:

   • Services reward users with tokens; users use them within services or sell them on exchanges.
   • Services acquire tokens from users or purchase them to maintain a sustainable reward system.

2. Ecosystem Activation Effects:

   • Token circulation promotes user engagement and service activation.
   • This contributes to token value stabilization and the sustainable growth of the ecosystem.