> For the complete documentation index, see [llms.txt](https://whitepaper.nudix.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://whitepaper.nudix.io/economic-model/programs-and-mechanisms-to-ensure-token-stability-and-liquidity.md).
# Programs and Mechanisms to Ensure Token Stability and Liquidity
**Vesting:** Vesting periods for team members and early investors with extended durations to ensure long-term commitment.
**Progressive Staking System on the Platform:**\
\
The staking system is built on a progressive model with thresholds and accelerated reward growth (bonding curve) to encourage users to lock tokens for extended periods.
**The key features include:**
* **Threshold Points:** Key lock-up durations (30, 90, 180, 365, 730, and 1095 days), with rewards increasing significantly upon reaching these milestones.
* **Smooth Progressive Growth:** An exponential acceleration formula between threshold points increases rewards gradually. The closer the user is to the next threshold, the higher the multiplier increment.
* **Calculation Mechanism:** Rewards are calculated daily based on the number of staked tokens and the current multiplier. The total reward depends on the lock-up duration and the chosen threshold.
**Example of a Basic Threshold Grid:**
| Lock-up Period | Multiplier (M) | Description |
| -------------------- | -------------- | -------------------------- |
| 30 days | 1.5x | Small jump |
| 90 days (quarter) | 3x | Significant jump |
| 180 days (half-year) | 6x | Next significant milestone |
| 365 days (year) | 12x | Annual multiplier |
| 730 days (2 years) | 25x | Long-term staking |
| 1095 days (3 years) | 50x | Maximum staking multiplier |
Note: A smooth bonding curve can be implemented between programs. For example, between 30 and 89 days, the multiplier grows gradually from 1.5x.
\
**Formula for Multiplier Calculation:**\
\
A formula can be applied to calculate the multiplier between thresholds, ensuring fairness and predictability in rewards.
$$
M\_d = M\_\text{start} + (M\_\text{end} - M\_\text{start}) \cdot \frac{\exp(k \cdot t) - 1}{\exp(k) - 1}
$$
Where:\
\
• *M**d* Multiplier for day *d*
• *M**start**, M**end**:* Multipliers for the start and end thresholds of the interval
• *t = (d - d\_start) / (d\_end - d\_start):* Normalized day within the interval
• *k*: Sharpness coefficient, regulating the growth acceleration
This formula defines the staking multiplier growth curve, ensuring a smooth transition between key intervals while incorporating sharp jumps at threshold points.
**Points Allocation for Staking**
Assume the reward logic (airdrop) operates through a system of "points." The longer and larger the staking commitment, the more points a user accumulates. At the end of each year, the total pool of points across all users is calculated, and the airdrop is distributed proportionally based on these points.
**Basic Formula for Daily Points**
Suppose a user stakes S tokens for D days, selecting the corresponding curve with a maximum multiplier M. Daily points can be calculated as:
$$
Daily Points=α×S×M
d
$$
Where:
* *α* — base constant
* *S* — number of staked tokens
* M*d* — current multiplier (depending of the elapsed staking days and the bonding curve)
**Additional Points and Badges**
To increase engagement, we introduce bonus badges that also grant points (either as standalone rewards or as additional multipliers).
**Examples include:**
1. Badge "30-day Lock": If a user stakes tokens for at least 30+ days within a year, they earn +500 bonus points.
2. Badge "Long Staker": Users who stake for 180+ days receive additional +N+N+N bonus points or a multiplier boost during the final airdrop distribution.
3. Referral Badge: For each referral who also locks tokens for 30+ days, the user earns +300 points or an additional coefficient for the final airdrop calculation.
4. Purchases: Points are granted for specific amounts or numbers of purchases made on the platform.
5. Participation in Crowdinvesting: Points are awarded for one-time or active participation in crowdinvesting campaigns.
This system creates strong incentives for long-term token holding, improving liquidity and stability within the ecosystem. It operates through a proprietary smart contract.