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DeltaOne Calculations

This document explains the mathematical foundations and calculations used in the Hokusai protocol's DeltaOne token system.

Core Concepts​

DeltaOne Definition​

A DeltaOne token represents a unit of model improvement, where:

  • 1 DeltaOne = 1% improvement in model performance
  • Improvements are measured against baseline metrics
  • Performance is verified through oracle attestation

Supply Logic​

The total supply of DeltaOne tokens is determined by:

  • Base supply from model registration
  • Performance improvement rewards
  • AMM trading activity (sells reduce supply)
  • Treasury operations

Mathematical Formulas​

1. Performance Improvement Calculation​

Improvement = (New_Score - Baseline_Score) / Baseline_Score * 100
DeltaOnes = Improvement * Model_Weight

Where:

  • New_Score = Current model performance
  • Baseline_Score = Initial model performance
  • Model_Weight = Model complexity factor (1.0 - 2.0)

2. Reward Distribution​

Reward = Base_Reward * (1 + Improvement_Bonus) * Time_Factor

Where:

  • Base_Reward = Standard reward amount
  • Improvement_Bonus = Additional reward for significant improvements
  • Time_Factor = Time-based multiplier (0.8 - 1.2)

3. API Fee Impact on Price​

Fee_To_Reserve = API_Fee * Reserve_Rate
Price_Impact = Fee_To_Reserve / (CRR * Supply)

Where:

  • API_Fee = Fee collected from model usage
  • Reserve_Rate = Percentage to AMM reserve (20%)
  • CRR = Constant Reserve Ratio
  • Supply = Current token supply

Calculation Examples​

1. Model Improvement​

Baseline_Score = 0.85
New_Score = 0.92
Model_Weight = 1.5

Improvement = (0.92 - 0.85) / 0.85 * 100
           = 8.24%

DeltaOnes = 8.24 * 1.5
          = 12.36 DeltaOnes

2. Reward Distribution​

Base_Reward = 100 DeltaOnes
Improvement_Bonus = 0.2 (20% bonus)
Time_Factor = 1.1

Reward = 100 * (1 + 0.2) * 1.1
       = 132 DeltaOnes

3. Fee Impact Calculation​

API_Fee = $100 USDC
Reserve_Rate = 0.20 (20%)
CRR = 0.20
Supply = 1,000,000 tokens

Fee_To_Reserve = 100 * 0.20 = $20 USDC
Price_Impact = 20 / (0.20 * 1,000,000)
            = 0.0001 USDC per token increase

Implementation Details​

Smart Contract Integration​

function calculateImprovement(
    uint256 newScore,
    uint256 baselineScore,
    uint256 modelWeight
) public pure returns (uint256) {
    uint256 improvement = ((newScore - baselineScore) * 100) / baselineScore;
    return (improvement * modelWeight) / 100;
}

function calculateReward(
    uint256 baseReward,
    uint256 improvementBonus,
    uint256 timeFactor
) public pure returns (uint256) {
    return (baseReward * (100 + improvementBonus) * timeFactor) / 100;
}

Oracle Integration​

  • Performance score verification
  • Improvement attestation
  • Fee flow monitoring

Monitoring and Analytics​

Key Metrics​

  • Total DeltaOne supply
  • Improvement distribution
  • API fee accumulation
  • Reward efficiency

Health Indicators​

  • Improvement rate
  • Reserve growth rate
  • Reward distribution
  • Model performance

Next Steps​

For additional support, contact our Support Team or join our Community Forum.

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