People Model Explainer

Understanding the Composite Index Formula for PAGI Tokenomics

COMPOSITE INDEX FORMULA
$$CI(t) = \alpha \sum_{i=1}^N H_i(t)\cdot q_i \;+\; \beta \sum_{j=1}^M A_j(t)\cdot w_j \;+\; \gamma S(H,A,t) \;+\; \delta E(t)$$

This formula ensures that the token value, reward distribution, or governance score reflects a balanced combination of holder behavior, ecosystem activity, and external market conditions.

1. Holder Contribution (H)

$$\alpha \sum_{i=1}^N H_i(t) \cdot q_i$$

Components:

  • $H_i(t)$: Metrics related to token holders at time $t$. Examples:
    • Token balance in wallet
    • Length of staking/holding
    • Reputation or past governance participation
  • $q_i$: Weight assigned to each holder metric.
  • $\alpha$: Scaling factor to control the overall influence of holder contributions.

Purpose: Rewards long-term commitment and strong community participation.

2. Activity Contribution (A)

$$\beta \sum_{j=1}^M A_j(t) \cdot w_j$$

Components:

  • $A_j(t)$: Metrics related to token activity and ecosystem usage. Examples:
    • Trading volume
    • Liquidity pool deposits
    • Smart contract interactions
    • DApp usage
  • $w_j$: Weight assigned to each activity variable.
  • $\beta$: Scaling factor for activity influence.

Purpose: Incentivizes ecosystem engagement and liquidity growth.

3. Synergy Effect (S)

$$\gamma S(H,A,t)$$

Represents non-linear interactions between holder behavior and ecosystem activity.

Examples:

  • Bonus rewards if a wallet both stakes tokens and provides liquidity.
  • Penalties if large holders trade against community interest.

$\gamma$: Coefficient controlling the impact of synergies.

Purpose: Encourages balanced participation across different token utilities.

4. External Factors (E)

$$\delta E(t)$$

Components:

  • $E(t)$: External influences outside the ecosystem. Examples:
    • Market volatility (BTC/ETH index)
    • Real-world economic signals (via oracles)
    • Regulatory or environmental conditions
  • $\delta$: Weight controlling the sensitivity of CI to external conditions.

Purpose: Makes the tokenomics model adaptive to real-world and crypto market conditions.

Summary

Holder contribution (α)

rewards loyalty & governance

Activity contribution (β)

drives liquidity & usage

Synergy effect (γ)

boosts multi-role engagement

External factors (δ)

aligns token value with broader environment

The Composite Index (CI) ensures that token distribution, value calculation, or governance scoring is:

  • Dynamic (updates in real-time with user actions and markets)
  • Fair (balances loyalty, activity, and synergy)
  • Sustainable (adapts to external economic conditions)