🔐Bonding Curve

The bonding curve system automatically adjusts token requirements for different membership tiers based on market conditions. Here's how it works:

The key innovation is that token requirements adjust inversely to price:

• When token price increases → required tokens decrease

• When token price decreases → required tokens increase

For example, if the token price doubles, you’ll need fewer tokens to maintain your tier.

🛡️ Built-in Protections

To ensure fair and stable adjustments, the system also applies:

✅ Rate Limits:

• Daily max change: 2%

• Biweekly max change: 10%

✅ Grace Periods:

• Verified users have a 7-day grace period before losing a tier.

• Users within 10% of the requirement retain their tier (if eligible).

✅ Dual Qualification:

• Users can qualify by either token count or USD value on holdings.

✅ Exponential Decay for Smooth Adjustments:

• The system uses exponential decay to adjust token requirements gradually based on price changes.

• This ensures no drastic jumps when token price fluctuates.

✅ Scaled Discounts:

• Fee discounts increase as your holdings grow:

  • Basic: 15-25% discount

  • Standard: 30-50% discount

  • Premium: 60-75% discount

• Role-based discounts override these if they offer better rates.

🎯 Why This Matters

This system ensures:

✔ Loyal holders are protected ✔ Tier requirements adjust smoothly with price changes. ✔ New users can still enter at reasonable token amounts.

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Graph Breakdown

• Dashed lines represent token requirements decreasing when price increases.

• Solid lines represent token requirements increasing when price decreases.

• Each color corresponds to a different membership tier (BASIC, STANDARD, PREMIUM).

• The black dotted line marks the target price ($1) where token requirements stabilize.

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Formulas

When Token Price Increases (Requirements Decrease):

• As the token price rises, the number of required tokens decreases towards the target minimum threshold using exponential decay:

$$T_{new} = T_{target} + (T_{previous} - T_{target}) \times e^{-k \times \left(\frac{P_{current}}{P_{target}}\right)}$$

Explanation:

• Tnew​ → The updated minimum token requirement

• Ttarget → The lowest possible token requirement for the tier

• Tprevious → The last recorded minimum requirement before price changes

• Pcurrent → The current token price

• Ptarget→ The price at which the tier requirement stabilizes

• k → A decay constant (default: 2) that controls the rate of adjustment

• ee→ Euler’s number (≈ 2.718), ensuring smooth decay

🔹 Result: If the token price doubles, the requirement moves closer to the target minimum (e.g., BASIC tier moves from 2500 tokens toward 250).

When Token Price Decreases (Requirements Increase)

$$T_{new} = \min \left( T_{start}, T_{previous} + (T_{start} - T_{previous}) \times e^{-k \times \left(1 - \frac{P_{current}}{P_{target}}\right)} \right)$$

Explanation:

• Tstart → The initial token requirement before any price-based adjustments

• Other variables remain the same as in the first formula.

🔹 Result: If the token price drops, the system increases token requirements gradually but prevents extreme jumps.