Automated Market Maker (AMM) Overview

INFORMATIONAL ONLY

This documentation explains the technical mechanics of the Hokusai AMM system. It is not investment advice. Trading tokens involves significant risk of loss. See the Investor Guide for complete risk disclosures.

The Hokusai AMM is a Constant Reserve Ratio (CRR) bonding curve that enables continuous buying and selling of model tokens using USDC. Each model has its own dedicated AMM pool, providing predictable pricing and always-available liquidity.

What is the Hokusai AMM?

The Hokusai AMM is an automated market maker built into every model token. It allows:

Buying tokens with USDC at a mathematically determined price
Selling tokens back to USDC under the active AMM pricing regime
API revenue integration that increases USDC reserves, supporting token value
Predictable pricing based on supply and reserve dynamics

Key Benefits

For Token Holders	For Model Contributors	For Investors
Always-available liquidity	Tokens have real market value	Transparent pricing
No need for order books	Can sell rewards for USDC	Continuous price discovery
API fees increase value	Flexibility in compensation	Participate in IBR or post-handoff trading
Deterministic pricing	Lower transaction costs	Support promising models

Why CRR Instead of Other AMMs?

The Hokusai protocol uses a Constant Reserve Ratio (CRR) bonding curve rather than traditional AMM models like Uniswap's Constant Product formula. Here's why:

Comparison with Other AMM Types

Feature	Hokusai CRR	Uniswap (x*y=k)	Order Book
Liquidity	Always available	Requires LPs	Requires orders
Price Discovery	Deterministic formula	Supply/demand	Bid/ask spread
Slippage	Predictable	Variable	Depends on depth
LP Needed?	No	Yes	No
Impermanent Loss	None (single-sided)	Yes (two-sided)	N/A
API Fee Integration	Direct to reserves	Goes to LPs	N/A

CRR Advantages

Single-Sided Liquidity: Only USDC reserves needed, no token-USDC pairs
Predictable Pricing: Mathematical formula makes prices deterministic
API Revenue Integration: Fees directly increase reserve backing
No Impermanent Loss: Single-asset model eliminates IL risk
Always Available: No need to bootstrap liquidity providers

How It Works: Before vs After AMM

Before: Burn-Only Model

[Earn Tokens] → [Hold] → [Burn for API Access]
     ↓
  No Exit

✅ Tokens earned for performance improvements
❌ No way to sell tokens
❌ No market price discovery
❌ API fees just collected, didn't affect token value

After: CRR AMM Model

[Earn Tokens] → [Hold] ←→ [Buy/Sell on AMM] ←→ [USDC]
     ↓             ↓            ↓
  Burn for     Liquidity   API Fees → Reserve ↑ → Price ↑
   Access

✅ Tokens earned for performance improvements
✅ Can sell tokens for USDC according to the AMM's current pricing regime
✅ Market price based on reserves and supply
✅ API fees increase reserves, raising token floor price

CRR Bonding Curve Mechanics

The AMM uses a Constant Reserve Ratio (CRR) formula where the ratio between USDC reserves and token market cap remains constant.

Visual: How Reserves Impact Price

Key Insight: API fee deposits increase reserves WITHOUT minting tokens, creating stronger price appreciation than buy orders.

Numerical Example: Reserve Impact

Event	USDC Reserve	Token Supply	Spot Price	Change
Initial	$10,000	10,000	$0.333	-
After $1,000 buy	$11,000	11,000	$0.333	+0%
After $1,000 fee deposit	$11,000	10,000	$0.367	+10%

Why the difference?

Buy order: Both R and S increase proportionally, price stays similar
Fee deposit: Only R increases, price rises significantly

Core Formula

Constant: k = R^w × S

Where:
  R = USDC reserve balance
  S = Token supply
  w = Constant Reserve Ratio (CRR)
  k = Invariant constant

Buy Formula

When you buy tokens by depositing USDC:

T = S × ((1 + E/R)^w - 1)

Where:
  T = Tokens minted
  S = Current supply before purchase
  R = Current reserve before purchase
  E = USDC deposited
  w = CRR (typically 10-30%)

Example: Buying with 1,000 USDC when R=100,000, S=1,000,000, w=0.2:

T = 1,000,000 × ((1 + 1,000/100,000)^0.2 - 1)
T = 1,000,000 × ((1.01)^0.2 - 1)
T = 1,000,000 × (1.00199 - 1)
T ≈ 1,990 tokens

Sell Formula

When you sell tokens back for USDC:

F = R × (1 - (1 - T/S)^(1/w))

Where:
  F = USDC returned
  T = Tokens burned
  S = Current supply before sale
  R = Current reserve before sale
  w = CRR

Example: Selling 1,990 tokens when R=101,000, S=1,001,990, w=0.2:

F = 101,000 × (1 - (1 - 1,990/1,001,990)^(1/0.2))
F = 101,000 × (1 - (0.998013)^5)
F ≈ 995 USDC (after fees)

Spot Price

The current price per token at any moment:

P = R / (w × S)

Where:
  P = Spot price (USDC per token)
  R = Current reserve
  S = Current supply
  w = CRR

Example: When R=100,000, S=1,000,000, w=0.2:

P = 100,000 / (0.2 × 1,000,000)
P = 100,000 / 200,000
P = 0.5 USDC per token

Initial Bonding Ratio (IBR) Phase

Every new model token starts on a flat launch curve before CRR pricing takes over.

Launch: IBR starts at $0.01/token
During IBR: Reserves build toward $25,000 USDC
Handoff: IBR ends when reserves hit $25,000 or 7 days elapse
After handoff: Standard CRR bonding curve pricing

Why IBR exists

The launch phase:

✅ Gives the AMM a clear starting price of $0.01/token
✅ Builds initial USDC reserve depth
✅ Makes the handoff rule explicit: $25,000 reserve or 7-day cap
✅ Transitions to CRR pricing only after initial bootstrap conditions are met

Learn more: IBR Phase Guide

API Fee Integration

A key innovation of the Hokusai AMM is how API usage fees increase token value:

[Model Usage] → [API Fees Collected]
       ↓
[Convert to USDC] → [depositFees() to AMM]
       ↓
[Reserve Increases] → [Spot Price Increases]
       ↓
[Token Holders Benefit]

How Fees Affect Price

When API fees are deposited:

Reserve (R) increases
Supply (S) stays constant
Spot price P = R / (w × S) increases proportionally

Example: Reserve increases by 10%:

Before: P = 100,000 / (0.2 × 1,000,000) = 0.5 USDC
After:  P = 110,000 / (0.2 × 1,000,000) = 0.55 USDC
Result: +10% price increase

Learn more: API Fee Flow

Fee Structure

The system has two separate fee mechanisms - don't confuse them:

1. AMM Trading Fees (when buying/selling tokens on AMM)

Trade Fees:

Default: 0.30% per trade
Maximum: 10% (governance-controlled)
Applied to: Both buys and sells on the AMM
Purpose: AMM sustainability

Example AMM Trade:

Buy: 1,000 USDC
Trade Fee (0.30%): 3.00 USDC
Net Deposited to Reserve: 997.00 USDC
Trade Fee Recipient: 3.00 USDC
Tokens Received: ~1,984 (calculated from buy formula)

AMM Launch Defaults

Parameter	Default
CRR	20% (`200,000 ppm`)
Trade fee	0.30% (`30 bps`)
Max IBR duration	7 days
Flat-curve threshold	$25,000 USDC
Flat-curve price	$0.01 per token

2. API Usage Fees (when using model API)

Separate from AMM trading fees, API usage fees are routed by UsageFeeRouter using cost-plus splitting first and infrastructureAccrualBps fallback second:

Primary path: InfrastructureCostOracle estimates cost per 1000 calls, and that cost accrues to InfrastructureReserve
Fallback path: If no oracle entry exists, infrastructureAccrualBps determines the split
Profit residual: Whatever remains is deposited to the AMM reserve and increases token backing

See Usage Fee Routing and API Fee Flow for details.

See API Fee Flow for complete details.

Security Features

The HokusaiAMM contract includes comprehensive security measures:

Slippage Protection

function buy(uint256 minTokens, uint256 deadline) external payable {
    require(tokensReceived >= minTokens, "Slippage too high");
    require(block.timestamp <= deadline, "Transaction expired");
    // ...
}

Protects against:

✅ Price movement during transaction
✅ Front-running attacks
✅ Stale transactions

Reentrancy Guards

All state-changing functions use OpenZeppelin's nonReentrant modifier to prevent reentrancy attacks.

Emergency Pause

Contract owner can pause trading in emergency situations while preserving user funds.

Parameter Bounds

CRR (w): 5% to 100%
Trade Fee: 0% to 10%

All parameters are governance-controlled with strict bounds.

User Personas and AMM

Data Suppliers

Earn: Tokens for improving model performance
Option 1: Hold tokens for long-term value
Option 2: Sell tokens on AMM for immediate USDC
Benefit: Flexible compensation choices

Model Developers

Launch: Deploy token with AMM
Benefit: Automatic liquidity for contributors
Control: Set initial parameters and IBR configuration
Growth: API fees increase token value automatically

Investors

Participate: During the IBR phase or after CRR handoff
Buy: Tokens at current bonding curve price
Support: Promising models with initial capital
Exit: Sell according to the active AMM pricing regime

Learn more: Investor Guide

Getting Started

For Buyers

Acquire USDC in your wallet
Navigate to the model's AMM page
Get a quote: How many tokens for X USDC?
Set slippage tolerance (e.g., 1%)
Execute buy transaction

Complete Buy Guide →

For Sellers

Check whether the AMM is still in IBR or has handed off to CRR pricing
Get a quote: How much USDC for Y tokens?
Approve token spending
Set slippage tolerance
Execute sell transaction

Complete Sell Guide →

Technical Resources

Smart Contracts

HokusaiAMM: Core AMM implementation with buy/sell/depositFees
HokusaiAMMFactory: Deploys new AMM pools for models
UsageFeeRouter: Routes API fees to AMM reserves

Contract Reference →

Formulas

Bonding Curve Math: Detailed Formulas
Price Impact: DeltaOne Calculations
Token Flow: Token Lifecycle

FAQ

Q: Can I lose money buying tokens?

Yes. Token prices can go down if:

Model usage decreases (fewer API fees)
More tokens are minted (supply increases)
Sellers exceed buyers

Q: What's the difference between "buying" and "minting"?

Minting: Creating new tokens as rewards for performance improvements (supply ↑)
Buying: Exchanging USDC for existing tokens via AMM (supply ↑, reserve ↑)

Q: Is the first week a sell lock?

No. The launch phase is the Initial Bonding Ratio (IBR) window: flat pricing at $0.01/token until reserves reach $25,000 USDC or 7 days elapse, then the AMM hands off to CRR pricing.

Q: What happens to API fees?

API fees are converted to USDC and deposited into the AMM reserve using depositFees(). This increases the reserve without minting tokens, raising the spot price.

Q: Who controls the AMM parameters?

Initially the model owner, later potentially transitioned to token holder governance.

Q: Is there a minimum or maximum trade size?

Yes, to prevent manipulation. Exact limits are set per model and governance-controlled.

Next Steps

Understand Formulas: Bonding Curve Mathematics
Launch Phase: Initial Bonding Ratio (IBR)
API Revenue: How Fees Increase Value
Start Trading: Buy Tokens Guide
Technical Deep Dive: HokusaiAMM Contract

For additional support, contact our Support Team or join our Community Forum.

What is the Hokusai AMM?​

Key Benefits​

Why CRR Instead of Other AMMs?​

Comparison with Other AMM Types​

CRR Advantages​

How It Works: Before vs After AMM​

Before: Burn-Only Model​

After: CRR AMM Model​

CRR Bonding Curve Mechanics​

Visual: How Reserves Impact Price​

Numerical Example: Reserve Impact​

Core Formula​

Buy Formula​

Sell Formula​

Spot Price​

Initial Bonding Ratio (IBR) Phase​

Why IBR exists​

API Fee Integration​

How Fees Affect Price​

Fee Structure​

1. AMM Trading Fees (when buying/selling tokens on AMM)​

AMM Launch Defaults​

2. API Usage Fees (when using model API)​

Security Features​

Slippage Protection​

Reentrancy Guards​

Emergency Pause​

Parameter Bounds​

User Personas and AMM​

Data Suppliers​

Model Developers​

Investors​

Getting Started​

For Buyers​

For Sellers​

Technical Resources​

Smart Contracts​

Formulas​

FAQ​

Q: Can I lose money buying tokens?​

Q: What's the difference between "buying" and "minting"?​

Q: Is the first week a sell lock?​

Q: What happens to API fees?​

Q: Who controls the AMM parameters?​

Q: Is there a minimum or maximum trade size?​

Next Steps​