Bonding Curve — Theory of Operation

Genesis Bonding Curve uses a x × y = k constant product pricing model with virtual reserves to enable deterministic, continuously-available token launches on Solana.

Summary

Genesis Bonding Curve uses a constant product AMM with virtual reserves to price a complete token sell-out at bounded, predictable prices.

• Constant product AMM — price rises as SOL flows in and falls as tokens are sold back, following x × y = k
• Virtual reserves — SOL and token reserves seeded at initialization to set a practical starting price and allow the curve to fully sell out
• Three lifecycle phases — Created → Active → Graduated; graduation fires automatically when all tokens are sold and migrates liquidity to a Raydium CPMM pool
• Two fee types — a protocol swap fee on every trade plus an optional creator fee; both apply to the SOL side and do not compound

For the raw swap formulas, reverse calculation math, and full account field reference, see Advanced Internals.

Constant Product AMM Pricing

Genesis Bonding Curve uses the same x × y = k formula used by Uniswap V2 and Raydium. The price at any moment is determined by the ratio of token reserves to SOL reserves — buying tokens reduces the token supply and raises the price; selling tokens increases the supply and lowers it.

Why Bonding Curves Require Virtual Reserves

A plain x × y = k curve has asymptotes at both ends that make it unsuitable for a sell-out launch. Standard AMMs avoid this by seeding real liquidity on both sides and never intending to fully sell out — slippage simply makes the extremes impractical to trade near. Bonding curve launches are different: they are designed to completely sell out.

• Bottom asymptote — with no SOL in the pool at launch, a buyer could drain all tokens for any nonzero SOL amount
• Top asymptote — the price of the last few tokens approaches infinity, making a full sell-out impossible at practical prices

Genesis Bonding Curve solves this by seeding the curve with virtual reserves — both virtual SOL and virtual tokens — that exist only in the pricing math. The virtual reserves set a finite starting price and shape the curve so that all real tokens can be sold through at practical, bounded prices.

Reserve Accounting

The curve maintains two sets of reserves that are combined for the AMM formula:

The effective reserves used in the AMM formula are:

totalSol    = virtualSol + realSol
totalTokens = virtualTokens + realTokens
k           = totalSol × totalTokens

A higher virtualSol relative to virtualTokens means a higher starting price. The current price in tokens per SOL is:

price = (virtualTokens + realTokens) / (virtualSol + realSol)

Fee Structure

Fees are applied to the SOL side of every swap, regardless of direction — deducted from SOL input on buys and from SOL output on sells.

Protocol Swap Fee and Creator Fee

Every swap is subject to a protocol swap fee. Creators can optionally add a creator fee on top:

Both fees are calculated independently on the gross SOL amount and do not compound. The net amount entering or leaving the curve is:

net = gross − protocolFee − creatorFee

For current protocol fee schedules, see the Protocol Fees page.

Fee Application by Trade Direction

Buy (SOL → tokens):

1. Fees are calculated on the gross SOL input
2. Fees are subtracted: amountInAfterFees = amountIn − fees
3. The AMM formula runs on amountInAfterFees
4. The buyer receives the full token output — no fee on the output side

Sell (tokens → SOL):

1. No fee on the token input — the full token amount enters the AMM
2. The AMM formula produces a gross SOL output
3. Fees are calculated on the gross SOL output
4. The seller receives: netSolOut = grossSolOut − fees

Graduation Fee

An additional fee is charged at graduation to cover the cost of initializing the Raydium CPMM liquidity pool. See Protocol Fees for the current rate.

First Buy Mechanism

The first buy mechanism allows a designated buyer to make a fee-free initial purchase when the curve is created.

When configured, the following rules apply:

1. Co-signature required — the designated buyer's wallet must co-sign the curve creation transaction
2. Fees waived — all fees (protocol swap fee and creator fee) are waived for this initial purchase only
3. One-time only — after the first buy completes, the mechanism is consumed; all subsequent swaps by any wallet, including the same buyer, are charged the normal fees

Bonding Curve Lifecycle

A Genesis Bonding Curve launch moves through three sequential phases:

Phase 1: Created

The curve is initialized with the token allocation, virtual reserve parameters, fee configuration, swap window start time, and any extensions (first buy, creator fee). No trading is possible yet.

Phase 2: Active

Once the configured start time is reached, users can buy and sell tokens freely. The price moves continuously according to the constant product formula as SOL flows in (buys) and out (sells). There is no deposit window — trading is always open while the curve is active.

Phase 3: Graduated

When all tokens on the curve have been sold, graduation fires automatically — no manual trigger is required. The accumulated real SOL is migrated into a Raydium CPMM pool for ongoing secondary trading. The bonding curve itself is closed.

Notes

• Virtual reserves exist only in the pricing math — they are never deposited onchain as real assets
• Creator fees are accrued in the bucket (creatorFeeAccrued), not transferred per-swap; see Creator Fees for configuration and claiming (claimBondingCurveCreatorFeeV2 / claimRaydiumCreatorFeeV2)
• Graduation fires automatically on full token exhaustion — no separate instruction is required
• The protocol swap fee rate is set by Metaplex and is not configurable by creators; see Protocol Fees for current rates
• The first buy mechanism is configured at curve creation and cannot be added after the fact
• For raw swap formulas, reverse calculation, and reserve exhaustion handling, see Advanced Internals

FAQ

What is the difference between a bonding curve launch and a launch pool?

A launch pool has a fixed deposit window and batch price discovery — users deposit during the window and receive tokens proportionally at a single clearing price. A bonding curve has no fixed window: users can buy and sell at any time after the swap window opens, with the price updating continuously after every trade.

Why does Genesis Bonding Curve use virtual reserves instead of a standard AMM?

A standard x × y = k curve approaches infinity at both extremes, making a complete sell-out impossible at practical prices. Virtual reserves (virtual SOL and virtual tokens added at initialization) anchor the curve with a finite starting price and shape it so that all real tokens can be sold through at bounded, predictable prices.

What triggers graduation and what happens to the accumulated SOL?

Graduation fires automatically when all tokens on the curve have been sold — no separate instruction is required. The accumulated real SOL is migrated into a Raydium CPMM pool for ongoing secondary trading, and the bonding curve account is closed.

Are the protocol fee and the creator fee compounded?

No. Both fees are calculated independently on the gross SOL amount of each swap. The net amount is gross − protocolFee − creatorFee. They do not compound.

Does the first buyer pay any fees?

No. When the first buy mechanism is configured, all fees are waived for that initial purchase. All subsequent swaps — including further buys from the same wallet — are charged the normal protocol and creator fees.

Glossary