The Math behind Pump.fun
If you’ve been off touching grass or living under a rock , let me introduce you to pump.fun .
The project created some waves amongst memecoin enthusiasts and is now being built across ecosystems like TON and Polkadot .
Pump.fun is a Solana-based marketplace that allows users to easily create and distribute their own tokens, most commonly “memecoins,” or tokens without an intrinsic value proposition beyond their novelty and community value.
At its core lies a concept called a bonding curve — a mathematical framework that dictates how tokens are created, valued, and traded within its ecosystem.
The math is mathing as user created tokens take surge over standard memecoins , skipping presales or team allocations. This minimizes rug pull risks and fosters a level playing field for all participants.
What in the crypto are Bonding Curves?
Bonding Curve is a mathematical concept that defines the relationship between the price and supply of an asset.
Bonding curve contracts are smart contracts that aim to create a market for tokens independent of crypto exchanges.
Unlike traditional cryptocurrencies or meme coins, where prices are often volatile and set by external market forces, bonding curves use mathematical formulas to determine token prices in a structured and transparent manner. This ensures that the value of tokens reflects the underlying dynamics of supply and demand within the platform itself.
TL;DR ?
The value of each token increases as number of tokens issued increases. This is caused because of limited supply.
In such scenarios , early participants tend to benefit the most.
Unlike many meme coins that rely on speculative trading and hype, Pump.fun employs a step function bonding curve to promote price stability and transparency.
How Does It Work?
- Understanding Bonding Curves: Bonding curves establish a direct relationship between token supply and price. As more tokens are minted (or burned), the price per token adjusts according to a predefined mathematical function.
- Step Function Dynamics in Pump.fun: Pump.fun’s step function bonding curve increments the token price in clear, predefined steps as more tokens are bought or sold. This approach provides clarity and predictability for participants within the ecosystem.
Let’s do the Math
Let’s illustrate how this might function in Pump.fun
Token Launch Process:
- When a coin is launched on Pump.fun, 800 million tokens are put into the bonding curve.
- All coins generated are identical, with a total of one billion tokens.
Sales and Bonding Curve Fulfillment:
- The objective after the coin launch is to promote and sell 800 million tokens.
- Once all 800 million tokens are sold, the bonding curve reaches full capacity and automatically transitions to Radium.
SOL Requirement for Radium Access:
- The approximate number of SOLs required to transition to Radium is 86.
- This number fluctuates slightly, typically between 84 and 86 SOL.
Market Cap Thresholds:
- Approximately 45 SOL is needed to reach the “King of the Hill” status, representing a halfway point in terms of token sales.
- Market cap thresholds trigger transitions in the bonding curve, with $69,000 for Solana and $420,000 for Blast.
Price Dynamics and Exponential Increase:
Token prices change exponentially based on a formula linked to the market cap. With the help of Julius AI and some reverse engineering a sample formula that can be used to replicate/estimate price is :
- The price per token increases significantly as the market cap grows, offering substantial returns for early investors.
Liquidity Provision and Burn Mechanism:
- When a token’s market capitalization hits specific thresholds ($69,000 for Solana, $420,000 for Blast), Pump.fun deposits liquidity ($12,000 for Solana, $30,000 for Blast) to decentralized exchanges (e.g., Raydium, Thruster DEX).
- This liquidity injection enhances trading activity and stability.
- A portion of deposited liquidity is burned, reducing token supply and potentially increasing its value.
How It Differs from Usual Meme Coins
- Price Stability: The structured nature of the bonding curve helps stabilize token prices by aligning them with the platform’s internal dynamics, reducing volatility commonly seen in meme coins.
- Transparency and Predictability: Participants can anticipate how token prices will adjust with each transaction, fostering trust and clarity within the ecosystem.
- Economic Alignment: The bonding curve incentivizes long-term engagement and investment by aligning token value with user participation and platform growth, rather than external market whims.
Resources for a deeper dive
- To better understand how bonding curves work, visualize them with graphs : Bonding Curve Visualizer by tokenlog.xyz
- https://docs.coinweb.io/learn/protocol/custom-tokens/token-bonding-curves