The Core Idea: A Mathematical Price Machine
Think of a Bonding Curve as a mathematical formula that automatically sets the price of a brand-new token based on how many tokens have been bought.

The fundamental rule is:
The more tokens people buy, the higher the price becomes.
The fewer tokens are in circulation, the cheaper the price is.
Pump.fun uses bonding curves to launch tokens in a fair, automated, and liquid way, without needing a traditional initial coin offering (ICO) or a centralized party setting the price.
How It Works on Pump.fun: A Two-Stage Process
Pump.fun's process is best understood in two key stages:
Stage 1: The Bonding Curve Phase (The "Pump")
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Token Creation: Someone creates a new meme token on Pump.fun. At this point, its market cap is zero, and the price is at its absolute lowest point on the curve.
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The Curve is Activated: When the first person buys the token, the bonding curve is activated. The price is determined by a formula (usually based on the total number of tokens bought and the market cap).
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The "Pump": As more and more people buy, they move up the curve. Because the supply is fixed at the start, increasing demand (buys) pushes the price up along the predetermined curve. This creates the exciting, "pumping" price action that the platform is named for.
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The Goal: The goal for early buyers is to get in at a low point on the curve and hope that later buyers push the price much higher.
Visualize it like this: Imagine a curve that starts almost flat and then curves upwards sharply. The first buyers are on the flat, cheap part. As people pile in, they push the price up the steep part of the curve.
Stage 2: The Liquidity Pool (LP) Migration (The "Fun")
This is the crucial endgame that makes Pump.fun unique.
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The Threshold: The bonding curve phase continues until the token's market cap reaches a specific goal (e.g., $69,000).
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Automatic Migration: Once the threshold is hit, the bonding curve phase ends. All the funds raised (in SOL) from the token sales are automatically used to create a liquidity pool (LP) on a real decentralized exchange (DEX), like Raydium.
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What This Means:
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For the Creator: They receive all the minted tokens, which they can now sell on the open market.
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For the Buyers: The token now has deep, real liquidity on a major DEX. They can freely trade their tokens without being restricted to the Pump.fun platform.
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For the Token: It "graduates" from being a Pump.fun experiment to a tradable asset on the open market.
A Simple Example
Let's say a new token $DOGECOIN3 is created.
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Price at Start: $0.0001
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You (Early Buyer): You buy $10 worth when the market cap is low. Because you're early on the curve, you get a large number of tokens.
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The Pump Begins: Other people see it and start buying. The price moves up the curve to $0.001, then $0.01.
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Late Buyer: Someone buys $10 worth now, but because the price is higher, they receive far fewer tokens than you did.
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Migration: The market cap hits $69,000. The liquidity pool is created on Raydium. The price is now set by normal market dynamics (supply and demand on the DEX). You can now sell your tokens on Raydium for a profit (if the price is higher than what you paid).
Why Bonding Curves are Perfect for Pump.fun
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Fair Launch (in theory): Everyone sees the same curve. The price is set by a transparent algorithm, not a central authority. The creator has to buy their own token to start the curve, just like everyone else.
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Instant Liquidity: During the bonding curve phase, you can always sell your tokens back to the curve. The sell price is determined by the same curve (and is always lower than the buy price), providing continuous, if imperfect, liquidity.
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Automation: The entire process from launch to DEX listing is handled by a smart contract, making it permissionless and efficient.
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Creates Hype & Gamification: The visible, rising price curve creates a sense of urgency and excitement, encouraging the "pump."
Crucial Risks to Understand
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Rug Pulls: The creator receives all the tokens upon migration. Nothing stops them from immediately dumping their entire holdings on the new liquidity pool, crashing the price to zero. This is the most common risk.
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Sell Pressure: When the token migrates to the DEX, there is often massive sell pressure from early buyers taking profits, which can crash the price.
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The Curve is a Trap: It's designed for the price to go up. If you buy at the top of the curve right before migration, you will almost certainly lose money, as the initial DEX price is often lower.
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No Utility: Most tokens on Pump.fun are pure memes with no fundamental value.
In summary, a bonding curve on Pump.fun is the automated engine that dictates the price of a new token during its initial launch phase, creating a gamified and liquid environment for speculation before it "graduates" to a full-fledged DEX.
