×
Mathematical Foundations

Math Understood Every Formula Explained

Dive deep into the mathematical foundations of $HEALTH Protocol. From cryptographic privacy guarantees to tokenomic incentives, understand how each formula powers the ecosystem. Whether you're an engineer, economist, investor, or just curious about earning rewardsโ€”the math is here.

๐Ÿ”

Cryptographic Identity Separation

Privacy & Security

Cryptographic Separation:

$\text{ProfileID} = \text{Hash}(\text{UserID} \parallel \text{salt} \parallel \text{secret})$
Click to explore โ†’

One-way transformation ensures complete separation between identity and health verification status. Privacy enforced by mathematics, not policy.

Quantum-resistant: Billions of years to reverse
Zero correlation: ProfileIDs cannot link to identities
๐Ÿ’Ž

Token Reward Algorithm

Rewards & Incentives

Reward Calculation:

$R = B \times M \times S$
Click to explore โ†’

Behavioral economics-based system that incentivizes consistent health verification through mathematically fair token distribution.

Regular test: 50 base reward
Optimal frequency: 1.5x multiplier
10-test streak: 2.0x multiplier
๐Ÿ”ฅ

Streak Multiplier Function

Rewards & Incentives

Logarithmic Scaling:

$S = 1 + \log_{10}(n)$
Click to explore โ†’

Logarithmic scaling rewards consistency while preventing system inflation. Meaningful rewards for dedication without breaking the economy.

10 tests โ†’ 2.0x
100 tests โ†’ 3.0x
1000 tests โ†’ 4.0x
โฐ

Grace Period Protection

Rewards & Incentives

Streak Protection:

$G(t) = \begin{cases} 1, & \text{if } t \leq t_{\text{grace}} \\ 1 - \frac{t - t_{\text{grace}}}{t_{\text{max}} - t_{\text{grace}}}, & \text{if } t_{\text{grace}} < t < t_{\text{max}} \\ 0, & \text{if } t \geq t_{\text{max}} \end{cases}$
Click to explore โ†’

Human-centered design with grace periods and gradual decay. Life happensโ€”the math accounts for it while encouraging consistency.

0-7 days late No penalty
7-30 days late Gradual decay
30+ days late Fresh start
๐Ÿ“‰

Emission Halving Schedule

Token Economics

Bitcoin-Inspired Sustainability:

$R_t = \frac{R_0}{2^{\lfloor t/p \rfloor}}$
Click to explore โ†’

Bitcoin-inspired halving mechanism ensures long-term sustainability. Early adopters benefit while controlling inflation and maintaining token value.

Year 1 100 tokens
Year 2 50 tokens
Year 3 25 tokens
Year 4 12.5 tokens
๐Ÿ”„

Points-to-Token Conversion

Token Economics

Dual-Layer System:

$T = P \times C \times L$
Click to explore โ†’

Dual-layer system allows everyone to participate. Earn points without crypto knowledge, convert to tokens when ready.

Simple entry: No wallet needed to start
Fair conversion: Liquidity-adjusted rates
๐Ÿ“Š

Quadratic Funding

Governance

Democratic Funding:

$G_i = M \times \frac{\sqrt{\sum_{j=1}^{n} c_{j,i}}}{\sum_{k=1}^{m} \sqrt{\sum_{j=1}^{n} c_{j,k}}}$
Click to explore โ†’

Democratic funding mechanism that prioritizes projects with broad community support over wealthy individual backing.

Square root equalizer: Community consensus matters more than wealth
๐Ÿ”’

Staking Rewards

Token Economics

Proportional Distribution:

$R_{staking} = B \times \frac{T_{staked}}{T_{total}} \times t$
Click to explore โ†’

Fair reward distribution for long-term token holders who help secure and stabilize the ecosystem through staking commitments.

More stake = More rewards
Longer commitment = Time bonus
Network growth = Value multiplier
๐Ÿ›๏ธ

Governance Maturity Score

Governance

Progressive Decentralization:

$M = \alpha N_{users} + \beta N_{integrations} + \gamma N_{providers}$
Click to explore โ†’

Decentralization tied to actual ecosystem growth. As more users and partners join, control gradually shifts to the community.

Users matter: More adoption = more decentralization
Real metrics: Not just time-based transitions
๐Ÿ“ˆ

Public Health Impact

Governance

Weighted Impact Measurement:

$I = \sum_{i=1}^{n} w_i \times m_i$
Click to explore โ†’

Weighted scoring system that quantifies real-world health outcomes to ensure protocol maintains mission alignment.

Testing frequency (30%)
Geographic reach (20%)
Provider network (20%)

$HEALTH Reward Calculator

See how your testing habits translate into token rewards and real value

Base reward varies by test type and verification method
More frequent testing = higher multipliers
Number of consecutive qualifying tests
Earlier years get higher base rewards

Your Rewards

0
$HEALTH Tokens

Annual Projection

0
$HEALTH per year
Based on current testing frequency

Want Even More Math?

This page covers the essential formulas, but there's much more depth in our complete technical documentation. Dive into cryptographic proofs, economic modeling, and the full technical specification.

๐Ÿ“‹

Complete Technical Spec

Every algorithm, variable, and design decision explained in detail

๐Ÿ”

Cryptographic Proofs

Zero-knowledge verification, hash functions, and privacy guarantees

๐Ÿ“Š

Economic Modeling

Token supply curves, inflation models, and value accrual mechanisms

๐Ÿ›๏ธ

Governance Design

Progressive decentralization, impact measurement, and community funding