Shadow Liquidity

The core innovation powering zero-capital prediction markets

Shadow Liquidity is a virtual AMM that simulates token reserves without requiring real capital. It enables permissionless market creation by bootstrapping liquidity through user participation.

The Core Concept

Traditional AMMs require locked liquidity—real tokens sitting in a contract. Shadow Liquidity uses virtual reserves that exist only as mathematical constructs:

---

How It Works

Initial State

Every market starts with identical virtual reserves:

Component	Initial Value	Purpose
virtualYES	1,000	Virtual YES token reserve
virtualNO	1,000	Virtual NO token reserve
k (constant)	1,000,000	CPMM invariant
vaultBalance	0	Real USDC from users
yesPrice	50%	Starting probability
noPrice	50%	Starting probability

---

The CPMM Formula

Prices are determined by the Constant Product Market Maker equation:

$$virtualYES \times virtualNO = k$$

When someone buys YES:

1. virtualYES decreases (user "receives" virtual tokens)

2. virtualNO increases (to maintain k)

3. YES price rises (less supply = higher price)

Pricing Formula

Price(YES) = virtualNO / (virtualYES + virtualNO)
Price(NO)  = virtualYES / (virtualYES + virtualNO)

// Example after buying YES:
virtualYES = 909
virtualNO  = 1,100
Price(YES) = 1,100 / 2,009 = 54.8%
Price(NO)  = 909 / 2,009 = 45.2%

Share Calculation

Slippage Example

---

The Vault & Solvency

What Happens to Your USDC?

All user deposits flow into a single vault. This vault pays out winners at resolution.

Solvency Equation

The protocol tracks solvency—the ratio of vault balance to maximum liability:

$$\text{Solvency} = \frac{\text{VaultBalance}}{\max(\text{TotalShadowYES}, \text{TotalShadowNO})} \times 100\%$$

Graduation Threshold: Markets graduate when:

1. Vault balance reaches bonding target (default $1,000, admin-configurable), AND

2. Solvency reaches 100% (vault can cover max payout), AND

3. Both sides have ≥20% of total shares (ensures two-sided market)

---

Example Walkthrough

Let's trace a complete buy transaction:

1

Start State

virtualYES: 1,000
virtualNO: 1,000
vaultBalance: 0 USDC
yesPrice: 50%

2

User Buys $100 YES

Fee: $0 (no fees during bonding!)
Net to vault: $100

3

Update Virtual Reserves

The Protocol calculates the new reserves and shares issued based on the Constant Product Formula ($x \times y = k$):

newVirtualNo = 1,000 + 100 = 1,100
newVirtualYes = 1M / 1,100 = 909.09

sharesReceived = 1,000 - 909.09 = 90.91 shares
avgPrice = $100 / 90.91 = $1.10

The price has effectively moved from 50% to 54.8%, reflecting the price impact of this trade.

4

Larger Trade Example ($1000 YES)

To better illustrate price impact and slippage, consider a larger purchase:

Fee: $0 (no fees during bonding)
Net Investment: $1000

newVirtualNo = 1,000 + 1,000 = 2,000
newVirtualYes = 1M / 2,000 = 500

Shares Issued = 1,000 - 500 = 500 shares
Avg Price = $1000 / 500 = $2.00 per share
New YES Price = 2,000 / 2,500 = 80%

5

Solvency Check

vaultBalance = $980
totalShadowYes = 971
totalShadowNo = 0
maxLiability = max(971, 0) = 971

Solvency = $980 / 971 = 100.9% ✓

Already solvent! Small trades graduate quickly.

---

Why It Works

🔐 Mathematical Solvency Guarantee

The CPMM formula creates a natural solvency buffer:

1. Users pay for shares

2. Slippage protects against one-sided markets

3. 20% minimum on each side ensures balance

4. Winners receive $1/share + OG bonus (Winner Profit Guarantee)

⚡ Zero Capital Barrier

No one needs to provide initial liquidity:

• Protocol initializes virtual reserves

• First trader sets the initial price movement

• Market naturally bootstraps through participation

• Creator pays nothing to launch

📈 Fair Price Discovery

CPMM ensures fair pricing:

• Large trades have proportionally more slippage

• Price converges to consensus probability

• No single actor can easily manipulate

• Arbitrage opportunities self-correct

---

Next Steps

📈 Bonding Curve Deep Dive

Advanced pricing mechanics and slippage analysis

🎓 Graduation Process

How markets transition to full trading