Weights

In the OXS ecosystem, setting and adjusting the weights for staking and yield farming rewards is crucial for a balanced and fair distribution of tokens. The weights, determined by specific formulas, ensure that participants receive rewards proportional to their contribution and the system's current state.

These formulas dynamically adjust based on actual participation versus ideal thresholds. If participation in staking or yield farming deviates from the desired levels, the weights shift to encourage or discourage more activity, maintaining equilibrium in the ecosystem. This adaptive approach ensures efficient and fair reward distribution, promoting sustained participation and liquidity while keeping the protocol stable and secure.

Formula for Weights

For Staking

$$\omega_{\text{staking}} = \begin{cases} \omega + M_{\text{staking}} \times \gamma_{\text{staking}} \times (T_{\text{staking}} - A_{\text{staking}})^\delta \\ \omega - M_{\text{staking}} \times \gamma_{\text{staking}} \times (A_{\text{staking}} - T_{\text{staking}})^\delta \\ \omega \end{cases}$$

• A_staking<T_staking

• A_staking>T_staking

• A_staking=T_staking

$$f(x) = x * e^{2 pi i \xi x}$$

For Yield Farming

$$\omega_{\text{yield}} = \begin{cases} \omega + M_{\text{yield}} \times \gamma_{\text{yield}} \times (T_{\text{yield}} - A_{\text{yield}})^\delta \\ \omega - M_{\text{yield}} \times \gamma_{\text{yield}} \times (A_{\text{yield}} - T_{\text{yield}})^\delta \\ \omega \end{cases}$$

• si A_yield < T_yield

• si A_yield > T_yield

• si (A_yield = T_yield

The weights for staking ( 𝜔 staking ω staking ​ ) and yield farming ( 𝜔 yield ω yield ​ ) are adjusted based on the difference between actual participation levels ( 𝐴 staking A staking ​ , 𝐴 yield A yield ​ ) and desired thresholds ( 𝑇 staking T staking ​ , 𝑇 yield T yield ​ ). The formula includes multipliers 𝑀 staking M staking ​ and 𝑀 yield M yield ​ , sensitivity coefficients 𝛾 staking γ staking ​ and 𝛾 yield γ yield ​ , and an exponent 𝛿 δ to determine how strongly the weights adjust when actual participation deviates from the ideal levels. If participation meets the threshold, the weight remains unchanged; if it deviates, the weight is adjusted up or down accordingly.

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