Bonding Curves

Logic underpinning the curves

Flat Curve

This flat bonding curve allows creators to bootstrap liquidity at a fixed price while enabling token migration and collateral transfer to a preferred DEX.

  • Migration Trigger: ~49% of the 1 billion token supply is sold.
  • Graduation Liquidity: Set by the creator (minimum 25SOL).
  • Creator Allocation: ~17.5% of the supply in Jupiter Lock, vested over 12 months with a 1-week cliff.
  • Market Cap (Mcap): 2 × Graduation Liquidity.

Key Metrics

  • Total Supply (T): 1,000,000,000 tokens
  • Market Cap (Fully Diluted): 2 × Graduation Liquidity
  • Token Price on Bonding Curve: Market Cap / Total Supply
  • Allocation at Migration (A): ~49% × Total Supply ≈ 490M
  • Max Allocation Before Migration: Up to 49.9% if a large buy occurs before the threshold
  • Flat Price Mechanics: Token price remains fixed until migration.

Migration Fee (F)

  • Raydium: 6 SOL (1 SOL → Raydium, 3 SOL → OpenBook, 2 SOL → Moonit)
  • Meteora: 3 SOL (1 SOL → Token accounts, 2 SOL → Moonit)

Calculations

Token Price at Migration: Price on Bonding Curve × 1.2

**Tokens to Burn (B): **B = T - A - M

Creator Allocation (Jupiter Lock): 45% × M

**Final Tokens Migrated: **Final Tokens Migrated = M - Creator Allocation

Final Token Price on DEX: (Collateral Collected - Migration Fees) / Final Tokens Migrated


Example Calculation (Devnet Token)

  • Token Address: 6YaxbM5KTC5hJVYsZFYtKRBJfYdWNaojjwtURBBDmoon
  • Total Supply (T) = 1,000,000,000
  • Graduation Liquidity = 25 SOL
  • Mcap (Fully Diluted) = 51.02 SOL
  • Price on Bonding Curve = 51.02 SOL / 1,000,000,000 = 51.02 lamports
  • Allocation at Migration (A) = 491,328,686 tokens
  • Collateral Shifted to Meteora = 25.07 - 3 = 22.07 SOL
  • Tokens to Migrate: 22.07 / (61.22 × 10^-9) ≈ 360M
  • Tokens to Burn: 1,000,000,000 - 491,328,686 - 360,000,000 = 148M
  • Creator Allocation: 45% × 360M ≈ 162M
  • Final Tokens Migrated to Meteora: 360M - 162M = 198M
  • Final Token Price on Meteora: 22.07 SOL / 198,000,000 = ~111 Lamports

Classic Curve

  • Migration Trigger: ~80% of 1B token supply is sold.
  • Market Cap at Migration: ~431 SOL.
  • Collateral Collected: ~88 SOL.
  • DEX Choice: Migration to Meteora or Raydium (set by the creator at launch).

Bonding Curve Formula

vTOKEN × vSOL = k

Where:

  • vTOKEN = Virtual reserve of the token.
  • vSOL = Virtual reserve of the collateral (SOL).
  • k = Constant determining the curve shape.

Setting Initial Values

k = vTOKEN × vSOL = iVTOKEN × iVSOL

Initial Price: iVSOL / iVTOKEN = 27.95 lamports

Initial Virtual Reserves: iVTOKEN = 1,073,000,000, iVSOL = 30 SOL

Key Metrics

  • Total Supply (T) = 1,000,000,000
  • Minimum Price = 27.95 lamports
  • Mcap at Migration = 431 SOL
  • Allocation at Migration (A) = ~80% of total supply
  • MarketCapThreshold = 345 SOL
  • Max Allocation Before Migration = 82% if a large buy occurs before the threshold
  • Curve Progress (%) = Allocation / Min Token Amount (799,820,983,207,404,442)

Migration Fee (F)

  • Raydium: 6 SOL (1 SOL → Raydium, 3 SOL → OpenBook, 2 SOL → Moonit).
  • Meteora: 3 SOL (1 SOL → Token accounts, 2 SOL → Moonit).

Calculations

Tokens to Migrate (M): (Collateral Collected - Migration Fees) / Price at Migration

Tokens to Burn (B): T - A - M


Example Calculation

  • Token Address: 6ovpeZNwNbXJzUaXMs8zozh9JvnJPq5teUJTQtLhRDwg
  • Total Supply (T) = 1,000,000,000
  • Allocation at Migration (A) = 801,085,146
  • Collateral Shifted to Raydium = 88.39 - 6 = 82.39 SOL
  • Price at Migration: (1,073,000,000 - 801,085,146) / (88.39 + 30) = 4.35e-7
  • Tokens to Migrate: 82.39 / 4.35e-7 ≈ 189M
  • Tokens to Burn: 1,000,000,000 - 801,085,146 - 189,228,531 = 9.69M