> For the complete documentation index, see [llms.txt](https://docs.fyuz.fun/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.fyuz.fun/how-fyuz-works/the-bonding-curve.md).

# 🧮 The bonding curve

Every Fyuz token trades on an automated **constant-product bonding curve** — the same model proven by Pump.fun, tuned for BNB Smart Chain.

## ➗ The math

The curve maintains the invariant **x · y = k**, where:

* **x** = virtual BNB reserve, starting at **8.25 BNB**
* **y** = virtual token reserve, starting at **1,073,000,000 tokens**

A buy adds BNB to x and removes tokens from y (price rises 📈). A sell does the reverse (price falls 📉). Every trade is priced deterministically by the invariant — no market makers, no spread, no order book.

## 👻 Virtual vs. real reserves

The *virtual* reserves exist to shape the price curve. The *real* token reserve — what can actually be bought — is **793,100,000 tokens** (79.3% of supply). The remaining **206,900,000 tokens** are reserved to seed the PancakeSwap pool at [graduation](/how-fyuz-works/graduation-to-pancakeswap.md).

| Parameter                | Value         |
| ------------------------ | ------------- |
| Total supply             | 1,000,000,000 |
| Virtual BNB (initial)    | 8.25 BNB      |
| Virtual tokens (initial) | 1,073,000,000 |
| Sellable on curve        | 793,100,000   |
| Reserved for LP          | 206,900,000   |

## 🏁 Opening price

At launch the implied market cap is `BNB price × 1B × 8.25 / 1.073B` ≈ **7.69 BNB** — a few thousand dollars, scaling with the BNB/USD price. From there, the only way the price moves is people trading.

{% hint style="info" %}
🛡️ Because the curve holds every BNB that was ever put in, **you can always sell**. There is no scenario where "liquidity leaves" while a token is on the curve.
{% endhint %}


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