chore(docs/multiplier-points.md): Fix formatting for GitHub Markdown

docs/multiplier-points.md

@@ -1,4 +1,4 @@
-# Understanding Multiplier Points (MP) and XP Rewards
+# Understanding Multiplier Points and XP Rewards
 
 ## Overview
 
@@ -8,49 +8,74 @@ This document explains:
 1. How MP determines XP rewards.
 2. How stake amount and lock-up duration affect MP.
 3. The role of Initial MP and Accrued MP.
-4. Examples illustrating how MP is calculated and accumulated over time.
+4. The relationship between XP tokens and the StakeManager.
+5. Examples illustrating how MP is calculated and accumulated over time.
 
 ## Key Concepts
 
 1. **Initial MP**: Multiplier Points issued immediately based on the stake amount and lock-up duration.
 2. **Accrued MP**: MP that accumulate over time as a function of the stake amount, elapsed time, and annual percentage
    yield (APY).
-3. **XP Rewards**: Determined by the total MP a user holds relative to the total MP in the system.
+3. **XP Tokens**: The token rewarded by the system.
+4. **XP Rewards**: Determined by the total MP a user holds relative to the total MP in the system.
 
 ## Formula for Multiplier Points
 
 ### Initial MP
 
-The formula for Initial MP is: \[ \text{Initial_MP} = \text{Stake} \times \left( 1 + \frac{100 \times
-T*{\text{lock}}}{100 \times T*{\text{year}}} \right) \]
+The formula for Initial MP is derived as follows:
+
+$$
+\text{MP}_\text{Initial} = \text{Stake} \times \left( 1 + \frac{\text{APY} \times T_\text{lock}}{100 \times T_\text{year}} \right)
+$$
 
 Where:
 
-- **Stake**: The amount of tokens staked.
-- **100% APY**: The annual percentage yield.
-- **\( T\_{\text{lock}} \)**: Lock-up duration in seconds.
-- **\( T\_{\text{year}} \)**: Total seconds in a year.
+- $Stake$: The amount of tokens staked.
+- $APY$: Annual Percentage Yield, set at 100%.
+- $T_{lock}$: Lock-up duration in seconds.
+- $T_{year}$: Total seconds in a year.
+
+This formula calculates the MP issued immediately when tokens are staked with a lock-up period.
 
 ### Accrued MP
 
-Accrued MP is calculated as: \[ \text{Accrued_MP} = \text{Stake} \times \frac{100 \times T*{\text{elapsed}}}{100 \times
-T*{\text{year}}} \]
+Accrued MP is calculated for time elapsed as:
+
+$$
+\text{MP}_\text{Accrued} = \text{Stake} \times \frac{\text{APY} \times T_\text{elapsed}}{100 \times T_\text{year}}
+$$
 
 Where:
 
-- **\( T\_{\text{elapsed}} \)**: Time elapsed since staking began.
+- $T_{elapsed}$: Time elapsed since staking began, measured in seconds.
+
+This formula adds MP as a function of time, rewarding users who keep their stake locked.
 
 ### Total MP
 
-Total MP is the sum of Initial MP and Accrued MP: \[ \text{Total_MP} = \text{Initial_MP} + \text{Accrued_MP} \]
+Total MP combines both Initial MP and Accrued MP:
+
+$$
+\text{MP}_\text{Total} = \text{MP}_\text{Initial} + \text{MP}_\text{Accrued}
+$$
+
+This total is used to calculate the user’s share of rewards.
 
 ## How MP Affects XP Rewards
 
-The rewards distributed in the system are proportional to each user’s MP. The reward share is calculated as: \[
-\text{Reward}_{\text{user}} = \text{Total_Rewards} \times \frac{\text{MP}_{\text{user}}}{\text{MP}\_{\text{total}}} \]
+The rewards distributed in the system are proportional to each user’s MP. The formula for reward share is:
+
+$$
+\text{Reward}_\text{user} = \text{Rewards}_\text{Total} \times \frac{\text{MP}_\text{user}}{\text{MP}_\text{total}}
+$$
+
+This ensures rewards are allocated based on the user’s contribution to the total MP.
 
 ## Examples
 
+Let’s consider three participants: Alice, Bob, and Charlie. The total reward pool is set at 10,000 XP tokens.
+
 ### Example 1: Alice
 
 - **Stake**: 100 tokens
@@ -59,16 +84,33 @@ The rewards distributed in the system are proportional to each user’s MP. The
 
 #### Initial MP
 
-Using the formula: \[ \text{Initial_MP} = 100 \times \left( 1 + \frac{100 \times 30}{100 \times 365} \right) \] \[
-\text{Initial_MP} = 100 \times \left( 1 + 0.082 \right) = 108.2 \]
+Using the formula:
+
+$$
+\text{MP}_\text{Initial} = 100 \times \left( 1 + \frac{100 \times 30}{100 \times 365} \right)
+$$
+
+$$
+\text{MP}_\text{Initial} = 100 \times \left( 1 + 0.082 \right) = 108.2
+$$
 
 #### Accrued MP
 
-\[ \text{Accrued_MP} = 100 \times \frac{100 \times 15}{100 \times 365} = 4.1 \]
+$$
+\text{MP}_\text{Accrued} = 100 \times \frac{100 \times 15}{100 \times 365} = 4.1
+$$
 
 #### Total MP
 
-\[ \text{Total_MP} = 108.2 + 4.1 = 112.3 \]
+$$
+\text{MP}_\text{Total} = 108.2 + 4.1 = 112.3
+$$
+
+#### Reward Share
+
+$$
+\text{Reward}_\text{Alice} = 10,000 \times \frac{112.3}{1,146.7} \approx 978.9
+$$
 
 ### Example 2: Bob
 
@@ -78,16 +120,31 @@ Using the formula: \[ \text{Initial_MP} = 100 \times \left( 1 + \frac{100 \times
 
 #### Initial MP
 
-\[ \text{Initial_MP} = 500 \times \left( 1 + \frac{100 \times 90}{100 \times 365} \right) \] \[ \text{Initial_MP} = 500
-\times \left( 1 + 0.247 \right) = 623.5 \]
+$$
+\text{MP}_\text{Initial} = 500 \times \left( 1 + \frac{100 \times 90}{100 \times 365} \right)
+$$
+
+$$
+\text{MP}_\text{Initial} = 500 \times \left( 1 + 0.247 \right) = 623.5
+$$
 
 #### Accrued MP
 
-\[ \text{Accrued_MP} = 500 \times \frac{100 \times 45}{100 \times 365} = 61.6 \]
+$$
+\text{MP}_\text{Accrued} = 500 \times \frac{100 \times 45}{100 \times 365} = 61.6
+$$
 
 #### Total MP
 
-\[ \text{Total_MP} = 623.5 + 61.6 = 685.1 \]
+$$
+\text{MP}_\text{Total} = 623.5 + 61.6 = 685.1
+$$
+
+#### Reward Share
+
+$$
+\text{Reward}_\text{Bob} = 10,000 \times \frac{685.1}{1,146.7} \approx 5,975.2
+$$
 
 ### Example 3: Charlie
 
@@ -97,19 +154,39 @@ Using the formula: \[ \text{Initial_MP} = 100 \times \left( 1 + \frac{100 \times
 
 #### Initial MP
 
-\[ \text{Initial_MP} = 300 \times \left( 1 + \frac{100 \times 0}{100 \times 365} \right) = 300 \]
+$$
+\text{MP}_\text{Initial} = 300 \times \left( 1 + \frac{100 \times 0}{100 \times 365} \right) = 300
+$$
 
 #### Accrued MP
 
-\[ \text{Accrued_MP} = 300 \times \frac{100 \times 60}{100 \times 365} = 49.3 \]
+$$
+\text{MP}_\text{Accrued} = 300 \times \frac{100 \times 60}{100 \times 365} = 49.3
+$$
 
 #### Total MP
 
-\[ \text{Total_MP} = 300 + 49.3 = 349.3 \]
+$$
+\text{MP}_\text{Total} = 300 + 49.3 = 349.3
+$$
+
+#### Reward Share
+
+$$
+\text{Reward}_\text{Charlie} = 10,000 \times \frac{349.3}{1,146.7} \approx 3,045.9
+$$
+
+### Total MP Calculation
+
+The total MP for all participants is:
+
+$$
+\text{MP}_\text{Total All} = 112.3 + 685.1 + 349.3 = 1,146.7
+$$
 
 ## Summary
 
 - **Initial MP** is based on the stake amount and lock-up time.
 - **Accrued MP** grows over time and adds to the staking power.
-- Longer lock-up durations grant more Initial MP, while time increases Accrued MP.
+- XP tokens rewards are proportional to their MP.
 - Total MP determines the share of XP rewards a participant earns.