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:

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How It Works

Initial State

Every market starts with identical virtual reserves:

Component	Initial Value	Purpose
virtualYES	100,000	Virtual YES token reserve
virtualNO	100,000	Virtual NO token reserve
k (constant)	10,000,000,000	CPMM invariant
vaultBalance	0	Real USDC from users
yesPrice	50%	Starting probability
noPrice	50%	Starting probability

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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 = 98,000
virtualNO  = 102,040
Price(YES) = 102,040 / 200,040 = 51%
Price(NO)  = 98,000 / 200,040 = 49%

Share Calculation

Slippage Example

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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 solvency reaches 100%, meaning the vault can cover the maximum possible payout.

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Example Walkthrough

Let's trace a complete buy transaction:

1

Start State

virtualYES: 100,000
virtualNO: 100,000
vaultBalance: 0 USDC
yesPrice: 50%

2

User Buys $100 YES

Fee: $100 × 2% = $2
Net to vault: $98

3

Update Virtual Reserves

newVirtualNo = 100,000 + 98 = 100,098
newVirtualYes = 10B / 100,098 = 99,902

sharesReceived = 100,000 - 99,902 = 98 shares
avgPrice = $98 / 98 shares = $1.00... wait, that's wrong!

Actually, let's recalculate properly:

The CPMM gives us shares based on the curve:
Δy = y - (k / (x + Δx))

With net $98 buying YES:
shares = 100,000 - (10B / (100,000 + 98))
shares ≈ 97.9 YES shares
avgPrice = $98 / 97.9 ≈ $1.00

Hmm, that's at 50%—let's see a bigger trade for clarity.

4

After $1000 YES Purchase

Fee: $20
Net: $980

newVirtualNo = 100,980
newVirtualYes = 10B / 100,980 = 99,029

Shares = 100,000 - 99,029 = 971 shares
Avg Price = $980 / 971 = $1.009 per share
New YES Price = 100,980 / 200,009 = 50.5%

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.

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Why It Works

🔐 Mathematical Solvency Guarantee

The CPMM formula plus the 2% fee creates a natural solvency buffer:

1. Users pay for shares

2. Fees accumulate in the vault

3. The vault always exceeds the maximum payout

4. Winners can always be paid $1 per share

⚡ 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

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Next Steps

📈 Bonding Curve Deep Dive

Advanced pricing mechanics and slippage analysis

🎓 Graduation Process

How markets transition to full trading