# 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.**

***

<figure><img src="https://3402603708-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fw9MVN5PhtEKd5VRPPnY2%2Fuploads%2F7Oobpd9AvIUs2CMbmWdz%2Fimage.png?alt=media&#x26;token=df9b9307-e3c1-4afd-8c25-701e7a413683" alt=""><figcaption></figcaption></figure>

#### 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.

***

## Formulas

### **When Token Price Increases (Requirements Decrease):**&#x20;

* 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.