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

# Bonding curve

> The verified endpoint-cp-v3 shifted constant-product model.

Each token uses a shifted constant-product curve with 18-decimal integer arithmetic.

## Constants

| Parameter                |                                         Value |
| ------------------------ | --------------------------------------------: |
| Total supply             |                          1,000,000,000 tokens |
| Curve allocation         |                            800,000,000 tokens |
| Graduation LP allocation |                            200,000,000 tokens |
| Virtual token reserve    |     `1,066,666,666.666666666666666667` tokens |
| Virtual ETH reserve      |                                         1 ETH |
| Net graduation reserve   |                                         3 ETH |
| Trading fee              | 1% of accepted buy gross or gross sell output |
| Initial reported price   |             `937,500,000` wei per whole token |
| Terminal reported price  |          `15,000,000,000` wei per whole token |

## Invariant

Let:

* `s` be sold curve tokens in base units;
* `r` be active ETH principal in wei;
* `Vt` be the virtual token reserve;
* `Ve` be the virtual ETH reserve;
* `K = Vt × Ve`.

The virtual coordinates are:

```text theme={null}
x = Vt - s
y = Ve + r
x × y ≈ K
```

The contract uses Solidity integer arithmetic. Outputs round down, while the post-trade virtual ETH coordinate uses ceiling division. Those rounding rules are part of the implementation.

For a nonterminal buy with net curve input `Δr`, the contract computes:

```text theme={null}
postVirtualTokens = ceil(K / (Ve + r + Δr))
tokensOut = (Vt - s) - postVirtualTokens
```

For a sell of `Δs` tokens:

```text theme={null}
postSold = s - Δs
postVirtualETH = ceil(K / (Vt - postSold))
grossETHOut = (Ve + r) - postVirtualETH
netSellerOutput = grossETHOut - fee
```

The reported spot price is `ceil((Ve + reserveCoordinate) × 1e18 / (Vt - s))` wei per whole token. Price rises as buys reduce virtual token inventory and add net reserve; sells reverse that movement before graduation.

<Warning>
  The curve formula does not guarantee value, liquidity at a desired price, or graduation. Transaction ordering and slippage can materially change execution.
</Warning>