What Are Bonding Curves?
A bonding curve is an automated market maker (AMM) that determines token price based on supply. As more tokens are bought, the price increases along a mathematical curve. As tokens are sold back, the price decreases. Think of it like this:- First buyer gets the cheapest price
- Last buyer before graduation pays the highest price
- Everyone in between pays fair market price based on current supply
Why Bonding Curves?
Fair Launch
No pre-sales, no insider allocations. The curve doesn’t care who you are, everyone pays the same price at the same supply level.Automatic Liquidity
The curve itself is the market maker. No need to seed liquidity pools or wait for market makers. Trading starts instantly.Immediate Trading
Buy and sell from day one
Always Liquid
Curve always provides liquidity
No Rug Risk
Liquidity locked in the curve
Fair Pricing
Math determines price, not humans
Price Discovery
Price finds its natural level based on net buying demand. High net demand (more buys than sells) -> price rises. Equal buys and sells -> price stays stable.No Rug Risk
Liquidity is locked in the curve until graduation. Creators can’t pull funds. The only way out is through trading or graduation.RektHub’s Bonding Curve Design
The Numbers
When you launch a token on RektHub:1
Total Supply: 1 Billion Tokens
Fixed supply, no inflation, no additional minting
2
Tradeable Supply: 850 Million
Available on the bonding curve for trading
3
Reserved Supply: 150 Million
Held for DEX graduation (creates liquidity pump)
4
Virtual Token Reserves: 1.073 Billion
Used for pricing calculations (smooth early prices)
5
Virtual Native Reserves: Varies by Chain
Calibrated for similar starting prices across all chains (~1.5 ETH equivalent)
Virtual Native Reserves by Chain
Virtual native reserves are calibrated per chain to maintain consistent pricing dynamics:- ETH-Based Chains
- Other Chains
All chains using ETH as native token:Applies to: Ethereum, Base, Arbitrum, Optimism, Zircuit, Lisk, Scroll (and their testnets)
Note: Throughout this documentation, we use 30 ETH in examples for easier
math visualization. On mainnet, RektHub uses 1.5 ETH for ETH-based chains,
which provides identical pricing curve dynamics.
Note: Throughout this documentation, we use 30 ETH in examples for easier
math visualization. On mainnet, RektHub uses ~1.5 ETH equivalent as the virtual
native reserve, which provides the same pricing curve dynamics with more
efficient capital allocation.
Virtual vs Real Reserves
Understanding the difference between virtual and real reserves is key to understanding bonding curves.- Real Reserves
- Virtual Reserves
- Why Virtual Reserves Matter
Real reserves are actual tokens and native currency in the curve contract.
These are what traders receive.
The Constant Product Formula
RektHub uses the time-tested constant product formula from Uniswap:- x = virtual native reserves
- y = virtual token reserves
- k = constant (product of x and y)
How buying works
How buying works
When you buy tokens:Note: This is a simplified calculation skeleton. The full implementation includes token transfers, edge case handling, and additional checks. See the contract on GitHub for the complete logic.
- Fee deducted from input first (0.99 ETH enters calculation)
- Native goes in -> x increases
- Tokens come out -> y decreases
- k stays constant (maintains the curve)
How selling works
How selling works
When you sell tokens:Note: This is a simplified calculation skeleton. The full implementation includes native transfers, reserve updates, fee distribution, and additional checks. See the contract on GitHub for the complete logic.
- Tokens go in -> y increases
- Native comes out -> x decreases (gross amount for k calculation)
- k stays constant
- Fee deducted from output (user receives 99% of calculated amount)
Price Discovery Example
Let’s trace how price evolves as a token gains traction:1
Launch (0 ETH traded in)
2
Early Stage (~9.9 ETH net traded in)
3
Growing (~99 ETH net traded in)
4
Bonding (850M tokens sold)
These are examples. Actual prices depend on trading volume and demand. The
curve ensures fair pricing at every stage. The graduation multiplier depends on
accumulated liquidity and the 12% migration fee.
The Trading Lifecycle
Phase 1: Active Trading
Your token launches with 850M tokens available on the curve. Anyone can buy or sell. Price moves up with buys, down with sells.- Buy Transaction
- Sell Transaction
Phase 2: Bonding Achieved
When 850 million real tokens are sold, your token is bonded. This means:All Supply Sold
All tradeable tokens have been purchased
Liquidity Accumulated
Mathematically determined amount of native currency
Ready for Graduation
Token can now migrate to a DEX
Trading Stops
No more buys/sells on the curve
Phase 3: Graduation to DEX
The creator triggers graduation. The remaining 150M tokens and accumulated native liquidity migrate to the chosen DEX.1
Migration Fee Charged
12% of liquidity (e.g., 13.72 ETH from 114.35 ETH)
2
Liquidity Sent to DEX
100.63 ETH + 150M tokens create LP position
3
LP Tokens Locked/Burned
No rug pull risk
4
Trading Opens on DEX
Token now tradeable on Uniswap/PancakeSwap/etc.
Why the graduation pump?
Why the graduation pump?
Multiple factors create upward price pressure:
- Instant liquidity depth: 88% of accumulated ETH creates strong buy support
- Supply squeeze: Only 150M tokens vs 850M that were on the curve
- FOMO effect: “I missed the curve, buying on DEX”
- Price discovery: New trading venue, new price action
Technical Deep Dive
Constants
Buy Calculation
Sell Calculation
Slippage Protection
Every trade includes aminOut parameter:
Why This Model Works
For Creators
For Creators
- No upfront capital needed (no liquidity to seed)
- Earn from every trade (30% of fees)
- Control graduation destination
- Massive migration reward (60% of 12% fee)
For Early Buyers
For Early Buyers
- Fair price at low supply
- Accumulate before bonding
- Benefit from graduation price bump
- Trade with confidence (liquidity locked)
For Communities
For Communities
- Everyone trades on equal terms
- Price reflects genuine demand
- No rug risk from liquidity pulls
- Clear path to DEX graduation
For The Ecosystem
For The Ecosystem
- Sustainable fee model funds development
- No platform token needed
- Scales to any chain with bonding curve support
- Proven mechanics, no experiments
Next Steps
Fee Structure
See exactly how fees are calculated and distributed
Token Migration
Learn about graduating to DEX
Start Building
Integrate bonding curves into your app
Contract Reference
Explore the BondingCurve contract