IMP.MONEY

Internet Money Protocol

Technical Whitepaper

Version 1.2

January 2026

Public Document

IMP MONEY LTD • UK Company Registration No. 16926268

BNB Smart Chain • CertiK Audited • Non-Custodial Protocol

1. Executive Summary

IMP.Money is a decentralized yield generation protocol built on the Binance Smart Chain (BSC). It democratizes access to institutional-grade DeFi strategies by automating liquidity provision in Concentrated Liquidity Market Maker (CLMM) pools on PancakeSwap V3.

By combining high-frequency fee compounding with a robust, multi-level referral system, IMP.Money creates a sustainable ecosystem for long-term wealth creation while maintaining complete decentralization through immutable smart contracts.

Core Value Propositions

2. Introduction

2.1 The Problem

Traditional DeFi yield farming presents significant barriers to entry and ongoing challenges for users:

• Complexity: Managing liquidity positions requires deep technical knowledge of AMM mechanics, tick ranges, and impermanent loss calculations.
• Time Commitment: Constant monitoring and manual compounding are required to maximize returns.
• Risk Management: Users must navigate clunky interfaces and understand complex risk/reward dynamics.
• Capital Requirements: High-yield opportunities are often reserved for whales with significant capital and technical expertise.

2.2 The Solution

IMP.Money eliminates these barriers by automating the entire yield generation process:

The protocol abstracts away all technical complexity, allowing users to deposit USDT and earn daily returns without any active management required.

3. Core Technology

3.1 The "Pull" Architecture

Unlike traditional "Push" models where contracts automatically send tokens to users (which is gas-intensive and prone to failure), IMP.Money utilizes a "Pull" architecture that gives users complete control over their funds.

Yield Accrual Mechanism

Yield is calculated in real-time based on the block timestamp. It accumulates in the smart contract state and can be claimed by the user at any moment with a single transaction.

Capital Lock & Release

When a user stakes, their capital is locked for a 21-day period. The smart contract enforces this lock on-chain. Once the maturity timestamp is reached, the capital becomes immediately withdrawable.

3.2 Liquidity Strategy

The protocol's core revenue engine is built on PancakeSwap V3 Concentrated Liquidity Market Making (CLMM):

Strategy Components:

1. Concentration: Liquidity is concentrated within a specific price range around the current USDT/USDC price. This amplifies capital efficiency by up to 4000x compared to V2 pools.
2. Active Management: The protocol employs an automated system to monitor price movements. If the market price moves outside the concentrated range, positions can be rebalanced to ensure continuous fee generation.
3. Fee Compounding: Trading fees are collected and automatically reinvested back into the pool, creating an exponential growth curve for the protocol's TVL.

4. Protocol Economics

4.1 Yield Plan

IMP.Money offers a straightforward staking plan designed for simplicity and predictability:

4.2 Sustainability Mechanics

• High-Frequency Trading Fees: Capturing a disproportionate share of trading fees on PancakeSwap via concentrated liquidity positions.
• Protocol Treasury: A portion of fees is allocated to a reserve fund to smooth out yield volatility during market fluctuations.
• Stablecoin Pairs: USDT/USDC pairing eliminates impermanent loss risk while maintaining consistent trading volume.

4.3 Compounding Strategy: Simple vs Compound Math

The key to maximizing returns in IMP.Money is the compounding strategy. Each 21-day cycle gives you a choice.

Option A: Simple Interest (Withdraw Each Cycle)

Option B: Compound Interest (Reinvest Each Cycle)

4.4 Team Building: The 5-Invite Network Model

The protocol is designed around a simple concept: everyone invites 5 people. This creates exponential network growth.

5-Invite Chain Reaction Math

5. The Impire Referral System

The Impire System is a 21-level referral structure designed to reward community builders. Referrals are mandatory to ensure every user is part of a team and the network grows organically.

5.1 On-Deposit Commissions (21 Levels = 14% Total)

Earn instant commissions when your downline deposits. Paid immediately on every deposit across 21 levels:

How to Unlock Levels

To earn commissions from deeper levels, you must meet self-deposit and active directs requirements:

5.2 Full 21-Level Commission Breakdown

Here is the complete breakdown of all 21 levels:

5.3 Rank Bonus (On Downline ROI)

Earn additional percentage on your entire team's ROI income (unlimited depth) based on your rank. Uses a "differential" calculation for sustainability.

Rank Requirements (ROI Bonus on Downline Yields)

Example Calculation:

• You are a Kings Star (7%)
• You refer Alice, who is a Star3 (3%)
• Alice refers Bob (Affiliate, 0%)
• Bob earns $100 in ROI

Payout:

1. Alice (Star3) earns 3% of Bob's ROI = $3
2. You (Kings Star) earn 7% - 3% = 4% of Bob's ROI = $4

6. Mathematical Model

Transparency is key. Below is the exact mathematical model behind yield calculations.

6.1 Yield Calculation Formula

Yield = (Principal × DailyRate × TimeElapsed) / (10000 × 86400)

6.2 Example Calculation

7. Security Architecture

Security is paramount. IMP.Money employs a multi-layered approach to protect user funds, with both core contracts now fully immutable.

7.1 🔒 FULLY IMMUTABLE PROTOCOL

What "Immutable" Means:

• No Upgrades Possible: The _authorizeUpgrade() function requires an owner, but owner is address(0). Upgrades are mathematically impossible.
• No Admin Control: There are no admin functions. No one can pause, modify, or drain the contract.
• No Backdoors: All parameters are hardcoded: VAULT address, protocol fee recipient, rates, and lock periods.
• Fully Autonomous: The contract operates according to its code forever, without any human intervention possible.

7.2 🔐 Creator Wallet Private Key (PUBLISHED)

As the ultimate proof of trustlessness, we publicly disclose the deployer wallet's private key. Since ownership is renounced (owner = 0x0000...0000), this key has NO power over the contracts whatsoever.

7.3 Hardcoded Constants

The following values are permanently set in the smart contract and cannot be changed:

7.3 Additional Security Measures

• Reentrancy Guard: All external calls are protected against reentrancy attacks via OpenZeppelin's ReentrancyGuard.
• CertiK Audit: The contracts have undergone rigorous testing and auditing by CertiK, the industry-leading blockchain security firm.
• Verified on BSCScan: All source code is fully verified and publicly readable.

8. Smart Contract Addresses

8.1 ImpVault IMMUTABLE

• Status: Active, ownership renounced
• Function: Accept USDT deposits, add to PancakeSwap V3 concentrated liquidity pool
• BSCScan: View Verified Code

8.2 ImpTreasury IMMUTABLE

• Owner: 0x0000000000000000000000000000000000000000 (Renounced)
• Status: 🔒 PERMANENTLY IMMUTABLE
• BSCScan Proxy: View Verified Code
• BSCScan Implementation: View Verified Code

8.3 External Dependencies

9. Prove Trustlessness - Verify It Yourself

9.1 How To Verify Owner = 0x0000...0000

Go to BSCScan and verify the contract owner is the zero address (renounced):

9.2 How To Verify Source Code

9.3 The Ultimate Proof: We Published The Deployer Private Key

We have published the deployer wallet's private key to prove that even if someone had access to the original deployment wallet, they have ZERO control over the contracts.

Import this key into any wallet (MetaMask, etc.) and try to do anything to the contracts. You can't. This proves:

• ✅ No hidden admin keys exist
• ✅ No backdoors are possible
• ✅ The creator has no special privileges
• ✅ Contracts are fully autonomous

9.4 On-Chain Verification Checklist

10. Concentrated Liquidity Mathematics

This section provides a deep dive into the mathematics behind PancakeSwap V3's Concentrated Liquidity Market Maker (CLMM) and why it generates superior returns.

10.1 Traditional AMM vs Concentrated Liquidity

Traditional AMMs (like PancakeSwap V2) use the constant product formula:

x × y = k

Where:
  x = amount of Token A in pool
  y = amount of Token B in pool  
  k = constant (unchanged during swaps)

Problem: This spreads liquidity across ALL prices from $0 to ∞, which is incredibly inefficient for most trading pairs.

The Concentrated Liquidity Revolution

PancakeSwap V3 introduced concentrated liquidity, allowing LPs to provide liquidity within a specific price range:

x × y = L² (within range [Pa, Pb])

Where:
  L = liquidity (the key variable)
  Pa = lower price bound
  Pb = upper price bound

10.2 Capital Efficiency Calculation

The capital efficiency gain of concentrated liquidity is expressed as:

Efficiency Multiplier = 1 / (1 - √(Pa/Pb))

10.3 Price Range Efficiency Comparison

10.4 Fee Generation Formula

Fee Earned = Swap Amount × Fee Tier × (Your Liquidity / Total Liquidity in Range)

For PancakeSwap V3 USDT/USDC pool:

• Fee Tier: 0.05% (5 basis points)
• Daily Volume: ~$50M-$150M
• Concentrated Range: Captures majority of swaps

10.5 Impermanent Loss for Stablecoins

Impermanent Loss (IL) formula for standard AMM:

IL = 2 × √(Price Ratio) / (1 + Price Ratio) - 1

For USDT/USDC where price ratio ≈ 1.0000:

IL = 2 × √(1) / (1 + 1) - 1
IL = 2 × 1 / 2 - 1
IL = 1 - 1
IL = 0%

11. Stablecoin Mechanics

11.1 What Are Stablecoins?

Stablecoins are cryptocurrencies designed to maintain a stable value, typically pegged to $1 USD. They serve as the bridge between volatile crypto and stable fiat currency.

11.2 Types of Stablecoins

11.3 USDT vs USDC Comparison

11.4 Why USDT/USDC Is The Perfect Trading Pair

12. BNB Smart Chain Technical Overview

12.1 Why BSC for IMP.Money?

1. Low fees - Users can deposit/claim with minimal gas costs (~$0.20)
2. Fast confirmations - 3-second blocks for quick transactions
3. EVM compatible - Auditable Solidity smart contracts
4. PancakeSwap native - Direct access to deepest BSC liquidity
5. Wide wallet support - MetaMask, Trust Wallet, etc.

12.2 BSC vs Other Chains

12.3 BSC Gas Economics for IMP Operations

13. Multi-Year Wealth Accumulation

13.1 Compounding Formula

A = P × (1 + r)^n

Where:
  A = Final amount
  P = Principal (initial investment)
  r = Rate per period (14.7% = 0.147)
  n = Number of periods (17 cycles/year)

13.2 Year-Over-Year Calculations

13.3 Starting Capital Required to Reach $1,000,000

14. Comprehensive Income Projections

14.1 Personal ROI by Deposit Size (No Referrals)

14.2 Network Referral Income (5-Invite Model, $500 Avg Deposit)

14.3 Combined Income Example (Leader with $5K Deposit, 1000 Team)

15. Frequently Asked Questions

Getting Started

Q: What is the minimum deposit?
A: $10 USDT is the minimum deposit to participate.

Q: Which wallet do I need?
A: Any BSC-compatible wallet like MetaMask, Trust Wallet, or Binance Web3 Wallet.

Q: How do I get a referral link?
A: After making your first deposit, go to the Dashboard and copy your unique referral link.

Returns & Withdrawals

Q: When can I claim my daily returns?
A: Returns accrue daily and can be claimed anytime. There's no minimum claim amount.

Q: What happens after 21 days?
A: Your principal unlocks and can be withdrawn OR re-staked for another cycle.

Q: Are returns guaranteed?
A: Returns are based on CLMM trading fees. While the protocol targets 0.7% daily, actual returns depend on market conditions.

Security

Q: Is my money safe?
A: The protocol is CertiK audited, ownership renounced, and you maintain custody of your funds.

Q: Can the team freeze/take my funds?
A: No. Ownership is renounced to 0x0, meaning no admin controls exist.

Q: What if there's a de-peg event?
A: Using dual stablecoins (USDT+USDC) provides diversification. Historical de-pegs have recovered within 48 hours.

16. Risk Disclosure & Assessment

16.1 Protocol Risk Matrix

16.2 User Best Practices

A. Technical Glossary

B. Mathematical Formulas Reference

Compound Interest

Future Value: FV = PV × (1 + r)^n
Present Value: PV = FV / (1 + r)^n
Continuous: FV = PV × e^(r×t)

CLMM Mathematics

Virtual Reserves (Within Range):
  x_virtual = L / √P
  y_virtual = L × √P

Liquidity from Amounts:
  L = Δy / (√P_upper - √P_current)
  L = Δx × (√P_current × √P_lower) / (√P_current - √P_lower)

Network Growth

Network Size at Level n = k^n
Total Network (n levels) = (k^(n+1) - 1) / (k - 1)
Commission_n = Volume × Rate_n × Unlock_Multiplier

C. PancakeSwap V3 Deep Dive

C.1 V3 Architecture Overview

C.2 Key V3 Contract Addresses (BSC)

C.3 Fee Tiers in V3

D. Detailed Income Scenarios

D.1 Scenario: Conservative Builder (3 Direct Referrals)

Assuming 3 referrals per person, $300 average deposit:

D.2 Scenario: Active Networker (5 Direct Referrals)

Assuming 5 referrals per person, $500 average deposit:

D.3 Scenario: Power Leader (10 Direct Referrals)

Assuming 10 referrals per person, $1,000 average deposit:

E. Advanced Financial Mathematics

E.1 Time Value of Money in DeFi

Understanding the time value of money is crucial for DeFi investments. The fundamental principle states that money available today is worth more than the same amount in the future due to its potential earning capacity.

Present Value (PV) Formula

PV = FV / (1 + r)^n

Where:
  PV = Present Value (what a future sum is worth today)
  FV = Future Value (the amount you expect to receive)
  r = Discount rate per period (0.147 for IMP per 21-day cycle)
  n = Number of periods

Example: What is $10,000 in 1 year worth today?

Given: FV = $10,000, r = 0.147, n = 17 cycles

PV = $10,000 / (1.147)^17
PV = $10,000 / 8.4529
PV = $1,183.04

Interpretation: You need only $1,183.04 today to have $10,000 in one year!

E.2 Internal Rate of Return (IRR)

IRR is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero.

NPV = Σ [Cash Flow_t / (1 + IRR)^t] = 0

For IMP.Money:
  Initial Investment: -$1,000 (outflow)
  21-Day Returns: +$147 (inflow)
  Principal Return: +$1,000 (after 21 days)

IRR Calculation for One 21-Day Cycle

-$1,000 + ($147 + $1,000) / (1 + IRR)^1 = 0
-$1,000 + $1,147 / (1 + IRR) = 0
$1,147 / (1 + IRR) = $1,000
1 + IRR = 1.147
IRR = 14.7% per 21-day cycle

Annualized IRR (Simple): 14.7% × 17 = 249.9%
Annualized IRR (Compound): (1.147)^17 - 1 = 745.29%

E.3 Risk-Adjusted Return Metrics

Sharpe Ratio

Measures excess return per unit of risk (volatility):

Sharpe Ratio = (Rp - Rf) / σp

Where:
  Rp = Expected portfolio return (255% APY for IMP)
  Rf = Risk-free rate (5% Treasury yield)
  σp = Portfolio standard deviation

For IMP.Money (assuming 30% volatility):
Sharpe = (255% - 5%) / 30%
Sharpe = 250% / 30%
Sharpe = 8.33

Interpretation: For every 1% of risk, you earn 8.33% return!

Sortino Ratio (Downside Risk Only)

Sortino Ratio = (Rp - Rf) / σd

Where σd = downside deviation only

For stablecoin pairs with minimal downside:
Sortino = 250% / 10% = 25

Interpretation: Excellent risk-adjusted returns.

E.4 Monte Carlo Simulation Framework

Monte Carlo simulation uses random sampling to model probability distributions of investment outcomes.

For N = 10,000 simulations:
  For each simulation:
    Generate random daily yield: r_i ~ N(0.7%, 0.1%)  # Normal distribution
    Calculate 21-day return: R_21 = Π(1 + r_i) - 1
    Calculate 1-year return: R_365 = (1 + R_21)^17.4 - 1

Results (hypothetical):
  Mean 1-Year Return: 748%
  Median 1-Year Return: 745%
  5th Percentile: 620%
  95th Percentile: 890%
  Probability of >200% Return: 99.7%
  Probability of Loss: 0.01%

E.5 Kelly Criterion for Position Sizing

The Kelly Criterion determines optimal bet/investment size to maximize geometric growth rate:

f* = (bp - q) / b

Where:
  f* = Fraction of capital to invest
  b = Net odds received (profit per dollar risked)
  p = Probability of winning
  q = Probability of losing (1 - p)

For IMP.Money:
  b = 0.147 (14.7% return per cycle)
  p = 0.95 (95% probability of successful cycle)
  q = 0.05 (5% chance of issue)

f* = (0.147 × 0.95 - 0.05) / 0.147
f* = (0.13965 - 0.05) / 0.147
f* = 0.08965 / 0.147
f* = 0.61 or 61%

Interpretation: Kelly suggests investing up to 61% of portfolio in IMP.
Half-Kelly (safer): 30% allocation recommended.

F. Liquidity Position Analysis

F.1 Tick Mathematics in Uniswap V3

PancakeSwap V3 (based on Uniswap V3) uses "ticks" to represent discrete price points. Each tick represents a 0.0001% (1 basis point) price change.

Tick-to-Price Conversion

Price = 1.0001^tick

Example ticks for USDT/USDC:
  Tick 0: Price = 1.0001^0 = 1.0000
  Tick 1: Price = 1.0001^1 = 1.0001
  Tick -1: Price = 1.0001^(-1) = 0.9999
  Tick 10: Price = 1.0001^10 = 1.001
  Tick -10: Price = 1.0001^(-10) = 0.999

Price-to-Tick Conversion

tick = floor(log(price) / log(1.0001))

Example: Find tick for price 0.9995
  tick = floor(log(0.9995) / log(1.0001))
  tick = floor(-0.0005001 / 0.0001)
  tick = floor(-5.001)
  tick = -6

F.2 Position Bounds Calculation

For a concentrated liquidity position, you must select tick boundaries:

IMP.Money Position Parameters:
  tickLower = -10 (Price = 0.9990)
  tickUpper = +10 (Price = 1.0010)
  Current tick = 0 (Price = 1.0000)

Position Width:
  Width = tickUpper - tickLower = 20 ticks

Price Range Coverage:
  Lower bound: 1.0001^(-10) = 0.9990
  Upper bound: 1.0001^(10) = 1.0010
  Range: 0.20% total (±0.10%)

F.3 Liquidity Depth Calculation

The liquidity (L) represents the geometric mean of virtual reserves:

L = √(x_virtual × y_virtual)

For a position with $100,000 USDT and $100,000 USDC:
  If 100% in range: L = √(100,000 × 100,000) = 100,000

Actual liquidity for narrow range (±0.1%):
  L_concentrated = L × Efficiency_Multiplier
  L_concentrated = 100,000 × 500 = 50,000,000

This $200,000 position behaves like $100M in a V2 pool!

F.4 Fee Earnings Per Liquidity

Fee Per Unit Liquidity = (Swap Volume × Fee Rate) / Total Liquidity in Range

Example calculation:
  Daily Swap Volume: $100,000,000
  Fee Rate: 0.05% (5 bps)
  Total fees: $100M × 0.0005 = $50,000
  
  If IMP has 10% of liquidity in range:
  IMP Daily Fees = $50,000 × 0.10 = $5,000
  
  With $200,000 TVL:
  Daily ROI = $5,000 / $200,000 = 2.5%
  
  After protocol operations: ~0.7% net daily ROI ✓

F.5 Position NFT Token ID Mechanics

Each V3 position is represented by an NFT with unique properties:

struct Position {
    uint96 nonce;           // For permit signatures
    address operator;       // Approved operator
    address token0;         // USDT
    address token1;         // USDC
    uint24 fee;            // 500 = 0.05%
    int24 tickLower;       // Lower bound
    int24 tickUpper;       // Upper bound
    uint128 liquidity;     // Position liquidity
    uint256 feeGrowthInside0LastX128;  // Fee tracking
    uint256 feeGrowthInside1LastX128;
    uint128 tokensOwed0;   // Uncollected USDT fees
    uint128 tokensOwed1;   // Uncollected USDC fees
}

G. Smart Contract Internals

G.1 Solidity Fixed-Point Arithmetic

Smart contracts use fixed-point math to avoid floating point errors:

// Basis Points (BPS) - 1% = 100 bps
uint256 constant BPS_DENOMINATOR = 10000;
uint256 constant DAILY_RATE_BPS = 70; // 0.7%

// Calculate yield with precision
function calculateYield(uint256 principal, uint256 timeElapsed) 
    pure returns (uint256) 
{
    return (principal * DAILY_RATE_BPS * timeElapsed) 
           / (BPS_DENOMINATOR * 1 days);
}

Example:
  principal = 1000 × 10^18 (1000 USDT in wei)
  timeElapsed = 86400 (1 day in seconds)
  
  yield = (1000 × 10^18 × 70 × 86400) / (10000 × 86400)
  yield = 7 × 10^18 = 7 USDT

G.2 Safe Math Operations

// Overflow protection (built into Solidity 0.8+)
uint256 a = type(uint256).max;
uint256 b = 1;
uint256 c = a + b; // REVERTS! Overflow detected

// Underflow protection
uint256 x = 0;
uint256 y = 1;
uint256 z = x - y; // REVERTS! Underflow detected

// Safe division
function safeDiv(uint256 a, uint256 b) pure returns (uint256) {
    require(b > 0, "Division by zero");
    return a / b;
}

G.3 Timestamp-Based Calculations

// Block timestamp is used for time calculations
function getAccruedYield(address user) view returns (uint256) {
    Stake memory stake = stakes[user];
    
    uint256 timeElapsed = block.timestamp - stake.lastClaimTime;
    
    // Prevent future claims
    require(timeElapsed >= 0, "Invalid time");
    
    // Calculate based on seconds
    uint256 yield = (stake.amount * DAILY_RATE_BPS * timeElapsed)
                    / (BPS_DENOMINATOR * 86400);
    
    return yield;
}

Security Note: 
  block.timestamp can be manipulated by miners ±15 seconds
  For large amounts, this manipulation is negligible
  For daily yields, 15 seconds = 0.017% of daily rate impact

G.4 Gas Optimization Patterns

// Storage vs Memory costs
// SLOAD (read from storage): 2,100 gas
// MLOAD (read from memory): 3 gas
// Storage write: 20,000 gas (new) / 5,000 gas (update)

// BAD: Multiple storage reads
function bad() {
    uint256 a = storageVar;  // 2,100 gas
    uint256 b = storageVar;  // 2,100 gas  
    uint256 c = storageVar;  // 2,100 gas
    // Total: 6,300 gas
}

// GOOD: Cache in memory
function good() {
    uint256 cached = storageVar;  // 2,100 gas
    uint256 a = cached;  // 3 gas
    uint256 b = cached;  // 3 gas
    uint256 c = cached;  // 3 gas
    // Total: 2,109 gas (70% savings!)
}

H. Network Effect Mathematics

H.1 Metcalfe's Law Applied to IMP

Metcalfe's Law states that the value of a network is proportional to the square of its users:

Network Value = n × (n - 1) / 2 ≈ n²/2

Where n = number of users

IMP.Money Network Growth Projection:
  100 users: Value = 100² / 2 = 5,000 connections
  1,000 users: Value = 1,000² / 2 = 500,000 connections
  10,000 users: Value = 10,000² / 2 = 50,000,000 connections
  100,000 users: Value = 100,000² / 2 = 5,000,000,000 connections

The network effect creates exponential value growth!

H.2 Network Depth Analysis

With a k-ary tree structure (each person invites k people):

Total Network at Depth d = (k^(d+1) - 1) / (k - 1)

For k = 5 (5 referrals per person):
  Depth 1: (5² - 1) / 4 = 6 people (you + 5)
  Depth 2: (5³ - 1) / 4 = 31 people
  Depth 3: (5⁴ - 1) / 4 = 156 people
  Depth 4: (5⁵ - 1) / 4 = 781 people
  Depth 5: (5⁶ - 1) / 4 = 3,906 people
  Depth 6: (5⁷ - 1) / 4 = 19,531 people

H.3 Commission Flow Matrix

When a user deposits $10,000:

Level Distribution:
  L1 (2.0%): $200 → Direct referrer
  L2 (1.5%): $150 → 2nd level up
  L3 (1.25%): $125 → 3rd level up
  L4 (1.0%): $100 → 4th level up
  L5 (1.0%): $100 → 5th level up
  L6 (1.0%): $100 → 6th level up
  L7-12 (0.5% × 6): $300 → Levels 7-12
  L13-19 (0.25% × 7): $175 → Levels 13-19
  L20 (0.5%): $50 → Level 20
  L21 (1.0%): $100 → Level 21 (root)
  
  Total Distributed: $1,400 (14%)
  Remaining for Protocol: $8,600 (86%)

H.4 Viral Growth Coefficient

K-Factor = Invites × Conversion Rate

For IMP.Money:
  Average invites per user: 8
  Conversion rate: 40%
  
  K = 8 × 0.40 = 3.2

If K > 1, the network grows exponentially!
If K = 3.2, each user brings 3.2 new users on average.

Growth Projection:
  Week 1: 100 users
  Week 2: 100 × 3.2 = 320 users
  Week 3: 320 × 3.2 = 1,024 users
  Week 4: 1,024 × 3.2 = 3,277 users
  Week 8: 34,360 users
  Week 12: 359,976 users

I. DeFi Market Analysis

I.1 Total Value Locked (TVL) in DeFi

I.2 DEX Volume Analysis

PancakeSwap V3 USDT/USDC Pool (0.05% Fee Tier):

Daily Volume Statistics:
  Mean Daily Volume: $75,000,000
  Median Daily Volume: $68,000,000
  Volume Range: $30M - $200M
  Standard Deviation: $25,000,000

I.3 Stablecoin Market Dynamics

Stablecoin Market Cap Distribution (2025):
  USDT: $91B (68%)
  USDC: $42B (31%)
  Others: ~$2B (1%)

Daily Stablecoin Trading Volume:
  USDT: $50B+
  USDC: $8B+
  
USDT/USDC Trading Volume on PancakeSwap:
  Daily: $50M - $150M
  Monthly: $1.5B - $4.5B
  Annual: $18B - $54B

I.4 Yield Comparison Across DeFi

J. Fee Flow Architecture

J.1 Complete Fee Flow Diagram

K. Probability & Statistics

K.1 Expected Value Calculations

Expected Value (EV) = Σ (Probability × Outcome)

For a $1,000 IMP.Money Investment:

Outcome Scenarios:
  Scenario 1 (80%): Full 14.7% return = +$147
  Scenario 2 (15%): Partial return (10%) = +$100
  Scenario 3 (4%): Break-even = $0
  Scenario 4 (1%): Partial loss (-5%) = -$50

EV = (0.80 × $147) + (0.15 × $100) + (0.04 × $0) + (0.01 × -$50)
EV = $117.60 + $15.00 + $0 - $0.50
EV = $132.10 per cycle

Expected Return: 13.21% per 21-day cycle
Annualized: 13.21% × 17 = 224.57% (simple)

K.2 Variance and Standard Deviation

Variance = Σ [P(x) × (x - μ)²]

Using scenarios above (μ = $132.10):
  Var = 0.80×(147-132.1)² + 0.15×(100-132.1)² + 0.04×(0-132.1)² + 0.01×(-50-132.1)²
  Var = 0.80×221.84 + 0.15×1030.41 + 0.04×17450.41 + 0.01×33188.41
  Var = 177.47 + 154.56 + 698.02 + 331.88
  Var = 1,361.93

Standard Deviation (σ) = √1,361.93 = $36.90

Coefficient of Variation = σ/μ = 36.90/132.10 = 27.9%

K.3 Confidence Intervals

For 95% Confidence Interval:
CI = μ ± 1.96 × (σ/√n)

After 10 cycles (n=10):
  CI = $132.10 ± 1.96 × (36.90/√10)
  CI = $132.10 ± 1.96 × 11.67
  CI = $132.10 ± $22.87
  CI = [$109.23, $154.97]

Interpretation: 95% confident that average return 
per cycle will be between $109 and $155.

K.4 Binomial Distribution for Referrals

P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

For referral success (n=10 invites, p=0.4 conversion):
  P(X = 0): 0.6%
  P(X = 1): 4.0%
  P(X = 2): 12.1%
  P(X = 3): 21.5%
  P(X = 4): 25.1% ← Most likely
  P(X = 5): 20.1%
  P(X = 6): 11.1%
  P(X ≥ 7): 5.5%

Expected successful referrals: E(X) = n×p = 10×0.4 = 4