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

# Bonding Curve

> How PNP uses a Pythagorean bonding curve AMM for continuous on-chain prediction market liquidity without order books.

## Bonding curve mechanism

PNP Exchange prices outcome tokens with a Pythagorean bonding curve—an on‑chain AMM that provides continuous liquidity from the first trade.
Prices adjust smoothly with supply, so users can buy or sell without a traditional order book.
Liquidity is built in, not borrowed from external market makers. We are also exploring delta‑neutral LP strategies to make providing liquidity safer.

## PNP Exchange makes liquidity mathematical.

![Screenshot of a deployment confirmation message that says All checks have passed.](https://mintcdn.com/pnpprotocol/ZlQJ3-9PwZkB8cbB/images/SS2.png?fit=max\&auto=format\&n=ZlQJ3-9PwZkB8cbB\&q=85\&s=2ac6e3d97187e7f42e58f12f1642821a)

### The Pythagorean Formula

The total reserve calculation follows this formula:

Where:

* `r` is the total reserve (capital) invested in the prediction market
* `s_yes`, `s_no`, `s_draw` are the supplies of YES, NO, and DRAW tokens respectively
* `c` is a coefficient that starts at 1 and gradually grows to account for accrued fees

We use a modified version of the pythagorean bonding curve with the constraint that Price(yes)^2 + Price(no)^2 == 1

### How it works

* Automatic pricing: Token prices adjust based on supply changes. More YES buys push YES up and NO down.
* Genesis liquidity: When a market is created with initial liquidity X, the creator receives equal amounts of YES and NO backed by reserve X.

## Why bonding curves power UGC markets

Bonding curves are a cornerstone of DeFi engineering. They turn market making into code and keep markets usable from day one.
We’re doubling down on advanced AMM design so USER-GENERATED-MARKETS can launch instantly, stay liquid, and scale to any niche.

### Benefits

* Fair price discovery: Prices reflect real demand and supply
* Sustainable economics: Trading fees accrue to the reserve and long‑term LPs

### Further reading

* Background on bonding‑curve prediction markets and the Pythagorean approach: [Introducing Prophet — Prediction Markets Based On Bonding Curves](https://blog.obyte.org/introducing-prophet-prediction-markets-based-on-bonding-curves-3716651db344)


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