Bonding Curve Mechanics

Overview

The bonding curve phase implements a virtual Constant Product Market Maker (CPMM) that determines share prices based on mathematical formulas rather than traditional order matching. This mechanism enables permissionless market creation without seed liquidity.

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Pricing Model

Constant Product Formula

The protocol maintains the invariant:

vYES × vNO = k

Price is derived as the marginal rate of exchange:

Price(YES) = vNO / (vYES + vNO)
Price(NO) = vYES / (vYES + vNO)

Price Impact

Each trade modifies the virtual reserves, shifting prices according to the constant product formula:

State	vYES	vNO	YES Price	NO Price
Initial	100,000	100,000	50.00%	50.00%
After $1k YES buy	99,030	100,980	50.49%	49.51%
After $5k YES buy	95,346	104,854	52.38%	47.62%
After $10k YES buy	91,116	109,754	54.63%	45.37%

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Trade Execution

Buy Order Processing

For a YES purchase of amount A:

1. fee = A × 0.02
2. net = A - fee  
3. vNO_new = vNO + net
4. vYES_new = k / vNO_new
5. shares = vYES_old - vYES_new
6. vault += A

Sell Order Processing

For selling S shares:

1. vYES_new = vYES + S
2. vNO_new = k / vYES_new
3. gross_payout = vNO_old - vNO_new
4. fee = gross_payout × 0.02
5. net_payout = gross_payout - fee
6. vault -= net_payout

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Slippage Analysis

Slippage increases non-linearly with trade size due to the constant product formula:

Trade Size (USDC)	Shares Received	Avg Price	Effective Slippage
$100	98.0	$1.020	2.0%
$500	485.2	$1.031	3.1%
$1,000	960.8	$1.041	4.1%
$5,000	4,654.0	$1.074	7.4%
$10,000	8,884.4	$1.126	12.6%

This slippage mechanism serves two critical functions:

1. Solvency Protection: Ensures vault accumulates faster than liabilities

2. Manipulation Resistance: Makes price manipulation economically costly

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Fee Structure

Operation	Fee Rate	Destination
Buy	2%	50% Creator / 50% Protocol
Sell	2%	50% Creator / 50% Protocol

The buy fee enhances solvency margin by increasing the vault balance relative to share issuance. The sell fee provides protocol revenue while discouraging excessive position churn.

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Early Exit Mechanism

Users may liquidate positions at any time during the bonding phase:

Exit Dynamics

• First-mover advantage: Early sellers receive better prices

• Slippage on exit: Large sell orders face price impact

• Vault protection: Payout limited by available reserves

Example: Selling 500 Shares

Metric	Before	After
vYES	99,000	99,500
vNO	101,010	100,503
Gross payout	—	$507.00
Fee (2%)	—	$10.14
Net payout	—	$496.86

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Bonding Phase Termination

The bonding phase ends under one of two conditions:

Condition 1: Graduation (Success)

Solvency >= 100%

Market transitions to Order Book trading with real tokens.

Condition 2: Deadline Expiry (Failure)

block.timestamp > bondingDeadline AND Solvency < 100%

Refund mode activates; users claim pro-rata share of vault.

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Economic Incentives

Actor	Incentive	Mechanism
Early buyers	Lower prices	CPMM starting at 50%
Large buyers	Price discovery	Market moves toward estimate
Arbitrageurs	Balance markets	Cheap side offers profit opportunity
Protocol	Solvency buffer	Fees accumulate in vault