> ## Documentation Index
> Fetch the complete documentation index at: https://docs.pumpevm.fun/llms.txt
> Use this file to discover all available pages before exploring further.

# Bonding curve mechanics

> Constant-product math behind launchpad pricing.

The launchpad uses a virtual-reserve constant-product bonding curve. Price discovery is continuous between buys and sells until the curve graduates to Uniswap V3.

## Parameters

| Parameter             | Value                |
| --------------------- | -------------------- |
| Virtual ETH Reserve   | 0.25 ETH             |
| Virtual Token Reserve | 1,073,000,191 tokens |
| Total Token Supply    | 1,000,000,000 tokens |
| Pre-Bond Target       | 0.03                 |
| Graduation Threshold  | 6.9 ETH              |
| Sell Fee              | 0.1% – 2% (dynamic)  |

## Formula

```text theme={null}
Price = (VirtualETH + RealETH) / (VirtualTokens + RealTokens)
```

Constant product is preserved on each trade:

```text theme={null}
(VirtualETH + RealETH) * (VirtualTokens + RealTokens) = k
```

## How it works

<Steps>
  <Step title="Initial state">
    Virtual ETH = 2.44, Virtual Tokens = 1,073,000,191, Real ETH = 0, Real Tokens = 0.
  </Step>

  <Step title="Buy">
    Real ETH increases, Real Tokens increase — price rises along the curve.
  </Step>

  <Step title="Sell">
    Real ETH decreases, Real Tokens decrease — price falls along the curve.
  </Step>

  <Step title="Graduation">
    When Real ETH reaches **6.9 ETH**, the curve can be finalized and liquidity migrates to a Uniswap V3 1% pool.
  </Step>
</Steps>