# Shadow Liquidity

{% hint style="info" %}
**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.
{% endhint %}

## 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:

{% @mermaid/diagram content="flowchart LR
subgraph Traditional\["Traditional AMM"]
T1\["Real Pool"]
T2\["1000 ETH + $2M USDC"]
T3\["Requires: $4M+ capital"]
T4\["High barrier"]
end

```
subgraph Shadow["Shadow Liquidity"]
    S1["Virtual Pool"]
    S2["1k vYES + 1k vNO"]
    S3["Requires: $0 capital"]
    S4["Anyone can create"]
end

style Traditional fill:#fef2f2,stroke:#ef4444,stroke-width:2px,color:#000000
style Shadow fill:#f0fdf4,stroke:#22c55e,stroke-width:2px,color:#000000
style T1 fill:transparent,color:#000000,stroke:none
style T2 fill:transparent,color:#000000,stroke:none
style T3 fill:transparent,color:#000000,stroke:none
style T4 fill:transparent,color:#000000,stroke:none
style S1 fill:transparent,color:#000000,stroke:none
style S2 fill:transparent,color:#000000,stroke:none
style S3 fill:transparent,color:#000000,stroke:none
style S4 fill:transparent,color:#000000,stroke:none" %}
```

***

## 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)

{% tabs %}
{% tab title="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%
```

{% endtab %}

{% tab title="Share Calculation" %}

```javascript
function buyShadowShares(side, usdcAmount) {
    // No fees during bonding phase!
    const netAmount = usdcAmount;
    
    if (side === 'yes') {
        // Buy YES = sell vYES to user
        const newVirtualNo = current.virtualNo + netAmount;
        const newVirtualYes = k / newVirtualNo;
        const sharesReceived = current.virtualYes - newVirtualYes;
        return sharesReceived;
    }
}
```

{% endtab %}

{% tab title="Slippage Example" %}
A $100 trade at different price points:

| Current Price | Shares Received | Avg Price | Slippage |
| ------------- | --------------- | --------- | -------- |
| 50%           | \~196 shares    | 51.0%     | 1.0%     |
| 60%           | \~163 shares    | 61.3%     | 1.3%     |
| 80%           | \~122 shares    | 82.0%     | 2.0%     |
| 90%           | \~109 shares    | 91.7%     | 1.7%     |

Slippage increases as you move the market more.
{% endtab %}
{% endtabs %}

***

## The Vault & Solvency

### What Happens to Your USDC?

{% @mermaid/diagram content="graph LR
A\[User: $100 USDC] -->|Buy YES| B\[Protocol]
B -->|$100| D\[Vault]
D -->|At Graduation| E\[2% Fee<br>to Protocol/Stakers/Creator]
D -->|At Resolution| F\[Pay Winners<br>Pro-rata split]" %}

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:

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

{% hint style="success" %}
**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)
   {% endhint %}

***

## Example Walkthrough

Let's trace a complete buy transaction:

{% stepper %}
{% step %}

#### Start State

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

{% endstep %}

{% step %}

#### User Buys $100 YES

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

{% endstep %}

{% step %}

#### 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.
{% endstep %}

{% step %}

#### 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%
```

{% endstep %}

{% step %}

#### Solvency Check

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

Solvency = $980 / 971 = 100.9% ✓
```

Already solvent! Small trades graduate quickly.
{% endstep %}
{% endstepper %}

***

## Why It Works

<details>

<summary><strong>🔐 Mathematical Solvency Guarantee</strong></summary>

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)

</details>

<details>

<summary><strong>⚡ Zero Capital Barrier</strong></summary>

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

</details>

<details>

<summary><strong>📈 Fair Price Discovery</strong></summary>

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

</details>

***

## Next Steps

<table data-card-size="large" data-view="cards"><thead><tr><th></th><th></th><th data-hidden data-card-target data-type="content-ref"></th></tr></thead><tbody><tr><td><strong>📈 Bonding Curve Deep Dive</strong></td><td>Advanced pricing mechanics and slippage analysis</td><td><a href="bonding-curve">bonding-curve</a></td></tr><tr><td><strong>🎓 Graduation Process</strong></td><td>How markets transition to full trading</td><td><a href="graduation">graduation</a></td></tr></tbody></table>