# Shiloh Yield Tokenomics (v1.02)  
**A Formal Specification of $SHILOH: Economic Model, Distribution, and Utility**

---

## 🔑 Token Overview

- **Token Name**: Shiloh Yield Token  
- **Ticker**: $SHILOH  
- **Total Supply**: \( S_0 = 500,\!000,\!000 \) (capped)  
- **Decimals**: 18  
- **Blockchain**: Ethereum (L1), with planned deployments on Polygon, Arbitrum, Optimism  
- **Contract Standard**: ERC-20 (non-rebasing, non-upgradeable)  

**Deflationary Guarantee**:  
\[
\forall t > T_{\text{Year1}}:\ \frac{dS}{dt} \leq 0
\]  
where \( S(t) \) = circulating supply at time \( t \), and \( T_{\text{Year1}} \) = 365 days post-launch.

---

## 💎 Token Distribution (Fair Launch)

| Allocation                  | Amount     | %   | Vesting / Release Conditions |
|----------------------------|------------|-----|------------------------------|
| Community Yield Farming    | 200,000,000| 40% | Linear over 12 months, weighted by:<br>\( w_{u,v,t} = \text{deposit}_u \times \text{duration}_u \times \text{riskTier}_v \) |
| Ecosystem & Development    | 150,000,000| 30% | 2–4 year linear vesting; milestone-based releases |
| Governance Reserve         | 75,000,000 | 15% | Multi-sig; DAO vote required for release |
| Treasury & Sustainability  | 75,000,000 | 15% | Multi-sig + 48h timelock; monthly transparency reports |
| **Founder**                | **0**      | **0%**| No allocation |
| **VC / Investors**         | **0**      | **0%**| No private sales |

**Total**: 500,000,000 (100%)

---

## 📈 Emission Schedule & Supply Dynamics

### Emission Function

Let \( E_0 \) = base monthly emission (Month 1). Then:

\[
E(t) = 
\begin{cases}
E_0 & \text{if } 0 < t \leq 3 \\
0.8 E_0 & \text{if } 3 < t \leq 6 \\
0.6 E_0 & \text{if } 6 < t \leq 9 \\
0.4 E_0 & \text{if } 9 < t \leq 12 \\
0.2 E_0 & \text{if } t > 12
\end{cases}
\]

Cumulative supply after Year 1:
\[
S(12) = \sum_{t=1}^{12} E(t) = 6.6 E_0 = 200,\!000,\!000 \quad \Rightarrow \quad E_0 \approx 30,\!303,\!030
\]

### Deflationary Mechanism

Protocol fees fund buybacks:

\[
B(t) = 0.4 \times \text{ProtocolFee}(t) = 0.4 \times 0.05 \times \text{NetProfit}(t)
\]

Tokens burned:
\[
\Delta S_{\text{burn}}(t) = \frac{B(t)}{P_{\text{SHILOH}}(t)}
\]

Net supply change:
\[
\Delta S(t) = E(t) - \Delta S_{\text{burn}}(t)
\]

Post-Year 1: \( E(t) = 0.2 E_0 \), but \( \Delta S_{\text{burn}}(t) \) typically exceeds emissions \( \Rightarrow \) **net deflation**.

---

## 🎯 Token Utility: Formal Economic Rights

### 1. Fee Participation (Cash Flow Rights)

Holders who stake $SHILOH in governance contract receive **pro-rata share** of fee-derived value via buybacks. The **effective yield** for a holder with balance \( h \) is:

\[
r_{\text{fee}}(t) = \frac{B(t)}{S_{\text{staked}}(t)} \cdot \frac{h}{S_{\text{staked}}(t)} \quad \text{(in USD terms)}
\]

### 2. Governance Voting

Voting power is **quadratic** to prevent whale dominance:

\[
v(h) = \min\left( \sqrt{h},\ 0.05 \cdot S_{\text{circ}} \right)
\]

Quorum: \( Q = 10,\!000,\!000 \) tokens must participate.  
Approval: >50% of votes cast.

### 3. Fee Reduction

Performance fee for user \( u \):

\[
f_u = 
\begin{cases}
0.05 & \text{if no \$SHILOH staked} \\
0.04 & \text{if staked, no lock} \\
0.035 & \text{if locked } \geq 6 \text{ months} \\
0.03 & \text{if locked } \geq 12 \text{ months}
\end{cases}
\]

Annual savings for $100K deposit @ 20% APY:  
- Max savings = \( 100,\!000 \times 0.20 \times (0.05 - 0.03) = \$400 \)

### 4. Yield Boost (Farming Multiplier)

Farming reward for user \( u \):

\[
R_u = R_{\text{base}} \cdot m(\tau)
\]

where lock duration \( \tau \) determines multiplier:

| \( \tau \)       | \( m(\tau) \) |
|------------------|---------------|
| 0                | 1.0           |
| >0               | 1.1           |
| ≥3 months        | 1.2           |
| ≥6 months        | 1.3           |
| ≥12 months       | 1.5           |

### 5. Priority Access

Early access window \( \delta \) (in days):

\[
\delta(h) = 
\begin{cases}
3 & \text{if } h \geq 50,\!000 \\
7 & \text{if } h \geq 100,\!000 \\
14 & \text{if } h \geq 500,\!000
\end{cases}
\]

### 6. Insurance Pool (Stablecoin-Denominated)

Users lock $SHILOH to provide coverage. Annual return:

\[
r_{\text{ins}}(v) = 0.05 + \rho(v)
\]

where \( \rho(v) \) = vault-specific premium:

| Vault             | \( \rho(v) \) |
|-------------------|---------------|
| StableVault       | 0.005         |
| BlueChipVault     | 0.01          |
| Top10Vault        | 0.015         |
| MemeVault         | 0.03          |
| HighRiskVault     | 0.05          |

**Claims paid in stablecoins**: 80% of loss covered.  
**Premiums collected in stablecoins**: No token price exposure.

---

## 🔐 Game-Theoretic Alignment

The founder's utility function is:

\[
U_{\text{founder}} = 
\begin{cases}
0 & \text{if Treasury} < \$50\text{K or no license} \\
\alpha \cdot \text{Treasury} & \text{if DAO-approved}
\end{cases}
\]

where \( \alpha \leq 0.2 \) (capped compensation).  
Thus, **maximizing \( U_{\text{founder}} \) requires maximizing protocol success**—a Nash equilibrium where all agents (founder, users, token holders) benefit from protocol growth.

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*Version 1.02 — Minor formatting improvements. All formulas properly LaTeX formatted. Aligned with BusinessPlan-v107.*