Memecoin manufacturing reveals: The mathematical principles behind bond curves, Pump.fun and running

Most memin guides introduce culture and community. This article describes the underlying mechanisms: the joint curve formula that sets prices, the graduation threshold that transfers tokens to real exchanges, and the mathematical logic that reveals why the vast majority of buyers have lost money before a single meme becomes popular.

Summary

The joint curve is a smart contract that mints tokens on demand. Each subsequent unit mints, the price will be higher than the previous one, eliminating the need for traditional order books or market makers.

Pump.fun is the largest memin launch platform. It allocates 800 million of the total supply of 1 billion per token to the joint curve. When the curve accumulates about 85 SOLs, the token will graduate to a decentralized exchange.

Less than 2% of all tokens launched on Pump.fun meet graduation conditions, which means that the vast majority of trading activity and losses occur during the joint curve stage.

"Carpet-pulling" behavior on the Joint Curve platform does not require removing liquidity in the traditional sense; it just requires insiders accumulating tokens cheaply at the bottom of the curve and then selling to the buying pressure of newcomers.

The mathematics of any convex joint curve dictates that later buyers will pay exponentially higher prices for each token than earlier buyers, creating a structural phenomenon of transferring value from latecomers to early participants, regardless of the creator's intentions.

Popular narratives portray memecoin as a joke about making money accidentally. Reality is more mechanical than this. Every memin traded on launch platforms such as Pump.fun follows the same mathematical structure that determines who makes money and who loses money-long before the first holder issued a rocket emoji. Understanding the union curve, the graduation process, and most of the wallet-concentration patterns that emerged before the crash is not an option for anyone investing money in this market.

What exactly does the joint curve do

The joint curve is a pricing function embedded in smart contracts. When a buyer sends SOL to the contract, the contract mints new tokens and sends them to the buyer at a price determined based on the number of tokens sold. When the seller sends the tokens back, the contract destroys them and returns SOL at the current curve price.

The simplest version of the formula is: Price = k * (supply sold)^n. In this formula, k is the scaling constant and n determines the steepness of the curve. When n equals 1, the price increases linearly with each token sold. When n is greater than 1, prices rise exponentially, which means that the gap between the price paid by early buyers and the price paid by later buyers widens sharply as more tokens enter circulation.

The key feature is that the contract itself holds reserves. There is no opponent. The SOL sent by the buyer is stored in the contract for the seller to withdraw during repurchase. This provides automatic liquidity at every price point on the curve, which is why joint curve tokens can be traded immediately after creation, without anyone pre-injecting into the liquidity pool.

The price is that this liquidity is very weak in design. Since prices are a function of cumulative supply, even medium-sized sell orders can significantly lower prices. A contract guarantees that you can sell, but it does not guarantee that the price you sell will be close to the price at which you bought.

How Pump.fun builds a token issuance

Pump.fun was launched on Solana in January 2024 and standardizes the minocoin creation process into a single transaction. The creator pays a small fee, names the token, uploads the image, and the platform deploys a joint curve contract with fixed parameters.

Each Pump.fun token has the same structure: a total supply of 1 billion tokens, without exception. Joint curve allocation: 800 million tokens enter the curve, which are available for purchase during the pre-graduation period. Graduation reserve: 200 million tokens are retained, which, together with the SOL accumulated in the curve, form the initial liquidity pool at the time of token graduation. Graduation threshold: Graduation is completed when Curve accumulates approximately 85 SOLs through purchase. At this point, the token "graduates" and moves to PumpSwap, the platform's own automated market maker. By March 2025, graduation fairs will send tokens to Raydium, a third-party decentralized exchange. Fees: Pump.fun charges a 1% fee for each transaction on the joint curve. This fee alone generated hundreds of millions of dollars in revenue during the platform's first year of operation.

Standardization is a key innovation. Because each token uses the same contract parameters, buyers do not need to audit smart contracts for hidden features. The risk plane shifts completely from contract codes to market dynamics and wallet distribution.

Graduation bottleneck

Graduation threshold is where theory and reality meet. Buying a total of 85 SOLs may not sound like much, but the graduation rate tells a different story.

Since January 2024, less than 2% of the millions of tokens issued on Pump.fun have met the graduation requirements. The remaining 98% died on the coalition curve, meaning they never accumulated enough buying pressure to move to a real trading venue.

For tokens that do graduate, this transition brings a structural shift. On the coalition curve, the contract itself provides liquidity. After graduation, liquidity depends on the pool injected by 200 million retained tokens and accumulated SOL. If the pool is small relative to the holder who wants to sell, the slip point at exit can be very serious.

Graduation events often trigger the first wave of selling. Early buyers who entered at the bottom of the curve now hold coins that have increased in value by several orders of magnitude. Many of them sell tokens into post-graduation liquidity pools, which drives down prices and traps subsequent buyers who buy near the top of the curve in the hope that graduation will be a catalyst for further gains.

The arithmetic of who wins and who loses

The convex form of the joint curve creates a mathematical certainty: the average buyer will lose money.

Consider a simplified example. Suppose the coalition curve of a certain token prices the first 100 million tokens at 0.00001 SOL each, and the last 100 million tokens at 0.0001 SOL each, an increase of 100 times. The first buyer spent 0.1 SOL to get 100 million tokens. The last buyer spent 10SOL to get 100 million tokens. Two buyers held the same amount of tokens, but the last buyer paid 100 times the price. If the price ends up lower than the entry price of the last buyer, the last buyer is at a loss. The first buyer can sell and make a profit at any price higher than 0.00001 SOL.

Zoom this pattern into thousands of buyers, and the pattern becomes clear: the coalition curve redistributes value from later buyers to early buyers. This is not a loophole, but the original intention of the mechanism. Curve incentivizes early participation by rewarding those who take risks when the token has no community, no narrative, and no transaction volume.

The problem is that the people who benefit the most from this structure are often the creators themselves and their affiliates, who can buy at the bottom of the curve in the same block where the token is deployed.

Now extends the arithmetic to the total amount of SOL stored in the curve. If the curve accumulated 85 SOLs before graduation, then these 85 SOLs would be the total capital base supporting all token holders. However, the implied market value of the tokens at the graduation price is much higher than 85 SOL because the market value is calculated by multiplying the final transaction price by the total supply. The gap between the implied market value and the actual SOL in the contract is the gap that makes the exit painful. There is not enough SOL in the system for every holder to sell at the final trading price. Someone must sell at a loss, and others may sell at a profit. The coalition curve does not create wealth; it simply redistributes the SOL that buyers deposit, minus the platform's 1% fee per transaction.

How does "carpet-pulling" work on the Joint Curve platform

Traditional "carpet-pulling" involves the creator removing liquidity from a decentralized exchange pool, making the token in the holder's hand impossible to sell. The Joint Curve platform has changed this dynamic.

At Pump.fun, joint curve contracts are standardized and cannot be modified by the creator after deployment. There is no liquidity to remove during the curve stage because the contract itself is liquidity. This has led many buyers to believe that they are protected from "carpet pulling" on the United Curve platform. But this is not the case.

There are three common forms of modern memin "carpet pulling": Internal accumulation: The creator or a coordinating organization uses multiple wallets to buy a large amount of available supply at the bottom of the curve. Since early curve prices were close to zero, obtaining 20% to 30% of the supply would cost very little SOL. Insiders then promote the token on social media to attract external buyers into the curve. As prices rise, insiders sell their positions back on the curve or on post-graduation DEX, withdrawing SOL deposited by subsequent buyers. Bundle issuance: Creators deploy tokens and buy large amounts of shares in the same transaction or block, ensuring that no one can buy before them. On-chain analysis tools can detect bundled transactions, but most retail buyers do not check them before buying. Post-graduation sell-off: After graduation, the creator's reserved allocations or accumulated positions are sold into the DEX liquidity pool. Because post-graduation pools are usually small, concentrated selling can drain the pool in seconds and cause prices to plummet. Tokens are still technically tradable, but the price is only a fraction of the graduation price.

None of this requires the creator to insert malicious code into the contract. Standardized contracts operate exactly as designed. Value extraction is achieved through market dynamics rather than technical loopholes.

Most on-chain signals that appeared before the crash

The advantage of the joint curve platform is that every transaction is public. The disadvantage is that most buyers never check the data.

Before the collapse of the memin, the following on-chain patterns appeared repeatedly: Wallet concentration: If the top ten wallets (excluding joint curve contracts) held more than 30% of the circulating supply, then the token was structurally very fragile. Coordinated selling from these wallets will overwhelm available liquidity. Creator Wallet Activity: Check whether deployer wallets or wallets funded from the same source have started selling. Blockchain browsers and specialized memin analysis tools can display wallet funds chains, revealing whether multiple "independent" buyers are actually controlled by the same entity. Speed of new currency holders: A sudden surge in new currency holders triggered by a single social media post or influencer promotion, followed by a platform period, suggests that buying pressure is temporary. The sustainable price behavior of joint curve tokens is usually manifested as a stable accumulation by the holder rather than a one-time explosion. Time between deployment and large transactions: Large purchases of tokens occur within minutes of deployment, often with coordinated internal purchases. Organic discoveries of new blockchain tokens rarely occur within the first block. Social media timing: Compare the time when the first large purchase appears on the chain to the time when the first promoted post appears on social media. If wallet accumulation precedes promotion hours or days, then the promotion is likely to be a distribution event rather than a discovery event.

What is not covered in this article

This guide explains the mechanism of the coalition curve, the economics of launch platforms, and the market dynamics that lead to losses. It does not cover: tax treatment of minicoin profits and losses, which varies by jurisdiction and is rapidly evolving. Social and cultural dynamics that determine which memocoins attract attention. Viral transmission is real and valuable, but it is not a mechanical process that can be analyzed like a joint curve. Ethereum, Base or other cross-chain memin platforms on the network. The core joint curve mechanism is similar, but the fee structure, graduation threshold, and DEX integration are different. Celebrity and influencer token issuance, which follows the same joint curve mechanism, but with additional reputational and legal considerations, is outside the scope of this guide.

Practical checklist before purchasing any memin

Before sending SOL to the joint curve, perform the following checks: Check holder distribution: Use the Solana blockchain browser or the miniin analysis dashboard to see how many wallets hold what percentage of the supply. If the distribution is highly concentrated, the risk of coordinated selling is high. Check bundled transactions: Check the previous transactions of tokens. If the creator's wallet or wallet funded from the same source purchases most of the supply in the deployment block, then the release is not organic. Check creator history: Most launch platforms track previous deployments in the creator's wallet. If the wallet has issued dozens of tokens and all collapsed in a short period of time, then the pattern is self-evident. Check curve position: Understand where current prices are on the combined curve. If the curve is 70% filled, you are paying much more than early buyers. The upside remaining before graduation may not justify the risk you will lose when the curve reverses. Set a loss limit before buying: Joint Curve tokens can lose 80% of their value in a matter of minutes. Decide how much you are willing to lose before buying, and sell if the token hits that level. The curve guarantees that you can sell, but it doesn't guarantee that you will sell. Know where you are on the curve: The percentage of the combined curve that has been filled tells you where you are in the buyer queue. If you buy when the curve is 90% filled, most of the upside from the initial price to the graduation price has been captured by early buyers. Your potential gain is limited to any premium the market offers after graduation, minus the slip point you will face when you sell to your post-graduation liquidity pool.

Matters to be concerned about

Regulatory concerns about launch platforms: The U.S. Securities and Exchange Commission (SEC) and international regulators have not yet taken formal action on the Joint Curve launch platform, but trading volume and the frequency of losses make regulatory review increasingly likely. Platform fee changes: Pump.fun's 1% transaction fee is an important source of revenue. A change in this fee, or the introduction of new fee structures on competing platforms, will change the economics of token creation and trading. Change of graduation destination: The migration from Raydium to PumpSwap in March 2025 changed the mobility after graduation. Further changes to the graduation mechanism or liquidity injection will affect the risk profile of tokens that reach the threshold. Anti-bundling tool: Multiple analytics platforms now automatically mark bundled releases. As these tools improve and become more widely used, the effectiveness of internal accumulation strategies may decline, but new methods of circumvention are likely to emerge. Cross-chain competition: Other joint curve launch platforms on the chain such as Base and Ethereum are gaining transaction volume. The fragmentation of memin transactions between chains will affect the depth of liquidity and graduation dynamics on each platform.

What is the joint curve in memin trading?

The joint curve is a mathematical formula embedded in a smart contract that sets the token price based on the number of tokens sold. As more tokens are purchased, prices rise along the curve. As tokens are sold back, prices fall. The contract itself holds the reserve currency (usually SOL) and provides automatic liquidity at each point on the curve.

How does Pump.fun work?

Pump.fun is a memin launch platform on Solana where anyone can create tokens for a small fee. The platform deploys a standardized joint curve contract with a total supply of 1 billion tokens, of which 800 million entered the curve. When purchases accumulated about 85 SOLs, the tokens graduated to PumpSwap, a decentralized exchange, and began trading with traditional pool-based liquidity.

What does it mean to graduate with memin?

Graduation refers to the moment when Joint Curve tokens accumulate enough buying volume and migrate from the internal trading mechanism of the launch platform to a decentralized exchange. At Pump.fun, this occurred at about 85 SOLs. After graduation, tokens are traded in a standard liquidity pool, which changes liquidity dynamics and price behavior.

Why do most memocoins fail?

Less than 2% of the tokens issued on Pump.fun meet the graduation requirements. Most tokens fail because they never attract enough buying interest to fill the coalition curve. Without sustained demand, prices will stagnate or fall as early buyers sell, and the tokens are technically still tradable, but the price is close to zero and are effectively abandoned.

Will I be "pulled carpet" on Pump.fun?

I will. Although Pump.fun uses standardized contracts to prevent creators from modifying code or removing liquidity from the joint curve,"carpet pulling" still occurs through market manipulation. Insiders buy large shares at the bottom of the curve, promote tokens to attract outside buyers, and then sell their positions into rising prices, withdrawing capital deposited by subsequent buyers.

How to identify memin before it "pulls the carpet" occurs?

Check whether the holder distribution is concentrated in a small number of wallets, check for bundled transactions in deployment blocks, review the history of previous releases of creator wallets, and check whether early buying activity appears to be coordinated. None of these signals guarantees that carpet pulling is imminent, but their presence significantly increases the probability.

What is the difference between a combination curve and a liquidity pool?

The joint curve uses mathematical formulas to cast and destroy tokens, with the contract itself acting as the only counterparty. A liquidity pool pairs two tokens in a smart contract, and the price is determined by the proportion of tokens in the pool. The joint curve provides liquidity from the time it is created without the need for external providers, and the liquidity pool requires someone to deposit two tokens to start trading.

Is buying early on the coalition curve a way to guarantee profits?

No. Buying early means you pay a lower price, but the token must attract enough subsequent buyers to push the price above your entry price for you to make a profit. Since more than 98% of Combined Curve tokens never meet the graduation requirements, the most common outcome for early buyers is that the token attracts very little interest and its investment approaches zero. Early entry improves the odds of winning compared with late entry, but the basic probability of failure is extremely high.

This document is for information purposes only and does not constitute any financial, investment or legal advice. Memin trading carries extremely high risks, including the possibility of losing all principal. Before making any investment decisions, be sure to study for yourself. The information is valid as of August 4, 2026.