> For the complete documentation index, see [llms.txt](https://onex-3.gitbook.io/onex-document/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://onex-3.gitbook.io/onex-document/coin/math-models.md).

# Math models

## 21.1 AMM Price Impact Formula (Corrected for V3)

For Uniswap V3-style concentrated liquidity (tick-based):

**V3 Virtual Reserve in Active Range:**

$$
x\_{virtual} = \frac{L}{\sqrt{P\_{current}}}
$$

$$
y\_{virtual} = L \times \sqrt{P\_{current}}
$$

where `L = liquidity position size`

**Price after sell of Δx tokens:**

$$
\sqrt{P\_{new}} = \sqrt{P\_{current}} - \frac{\Delta x}{L}
$$

$$
\text{Price Impact} = \frac{P\_{current} - P\_{new}}{P\_{current}}
$$

**Effective Liquidity Multiplier vs V2 (for ±5% range):**

$$
\text{Multiplier} \approx 10\times \text{ (validated — v1.0 figure correct)}
$$

This means concentrated liquidity provides approximately 10× more effective depth per dollar of capital vs. standard V2 AMMs.

***

## 21.2 Sell Tax Revenue Projection

Conservative assumptions:

* Average daily volume: $200,000
* Sell volume: 50% of total = $100,000/day
* Average blended tax: 5%

| Period  | Tax Revenue |
| ------- | ----------- |
| Daily   | $5,000      |
| Monthly | $150,000    |
| Annual  | $1,800,000  |

### Tax Distribution (Annual)

| Recipient             | Annual Amount |
| --------------------- | ------------- |
| ABR Buyback (30%)     | $540,000      |
| IEV Vault (25%)       | $450,000      |
| Staking Rewards (20%) | $360,000      |
| Liquidity Pool (15%)  | $270,000      |
| Treasury (10%)        | $180,000      |

***

## 21.3 Burn Rate Projection

| Burn Source                 | Year 1 Estimate                          |
| --------------------------- | ---------------------------------------- |
| ABR burns (40% of buyback)  | \~216,000 ONEx                           |
| IEV exits (50% burned)      | \~10,000,000 ONEx                        |
| SEM exits (40% burned)      | \~2,000,000 ONEx                         |
| ADTL ONEx tax (100% burned) | \~100,000 ONEx                           |
| **TOTAL Year 1**            | **\~12,316,000 ONEx (≈2.46% of supply)** |

### 5-Year Supply Trajectory

| Metric                     | Value              |
| -------------------------- | ------------------ |
| Start Supply               | 500,000,000 ONEx   |
| After 5 years (post-burn)  | \~460,000,000 ONEx |
| Staked/Locked              | 200,000,000+ ONEx  |
| Effective free circulating | \~260,000,000 ONEx |

***

## 21.4 Defense Budget at Launch (1 August 2027)

| Fund                           | Amount          |
| ------------------------------ | --------------- |
| Liquidity Pool Seeding (USDT)  | $4,000,000      |
| IEV Vault (seeded at launch)   | $1,800,000      |
| Automated Buyback Reactor      | $1,200,000      |
| Treasury Reserve (diversified) | $1,500,000      |
| Synthetic Exit Model Fund      | $1,000,000      |
| Bridge Insurance Fund          | $316,000        |
| Operations                     | $2,000,000      |
| Marketing                      | $500,000        |
| ZKPS Infrastructure            | $200,000        |
| AADE Infrastructure (Year 1)   | $184,000        |
| **TOTAL USDT DEPLOYED**        | **$12,700,000** |

### Monthly Defense Revenue (Ongoing)

| Source                           | Monthly Revenue |
| -------------------------------- | --------------- |
| Sell Tax Revenue                 | $150,000        |
| LP Fee Earnings (protocol-owned) | $30,000         |
| IEV Spread Revenue               | $50,000         |
| SEM Spread Revenue               | $25,000         |
| Ecosystem Revenue (growing)      | $50,000+        |
| **TOTAL MONTHLY ADDITION**       | **$305,000+**   |

**Year 1 Total Defense Capital:** \~$12.16M vs estimated daily trading volume $1–2M.

**Defense Fund = 6–12× Daily Volume = EXTREMELY ROBUST.**