uDOGE Technical Whitepaper

1. Philosophical Paradigm: Operatorless & Code as Law

uDOGE is a pristine social experiment in decentralized finance. The smart contracts contain no administrator, upgrade vectors, multi-sig backdoors, pre-mines, or team allocations. Once the core Hook contract is deployed and mint privileges are permanently bound, code remains the sole arbiter of execution on the blockchain. All commercial mechanics are dictated entirely by mathematical curves.

2. Asymptotic Mathematical Equations (Bonding Curve)

uDOGE adopts an elegant exponential distribution function. The asymptotic maximum token supply $K$ pays homage to the initial design parameters of Dogecoin:

By introducing a single global state variable, `ethCum` (denoted as $E$), representing the cumulative net ETH reserves deposited, the protocol state is strictly and uniquely bound:

• Cumulative Supply Equation: $q(E) = K \cdot (1 - e^{-E/S})$
• Marginal Price Equation: $p(E) = \frac{S}{K} \cdot e^{E/S} = \frac{S}{K - q}$
• Redeemable Reserve Equation: For a given current supply $q$, burning $b$ tokens yields a refund of: $$\Delta e(q, b) = S \cdot \ln\left(\frac{K - q + b}{K - q}\right)$$

3. Protocol Fee Allocation & Liquidity Backing

To secure the structural integrity and technical operations of the asymptotic reserve mechanism, a micro-fee layer is natively integrated:

Both buy and sell transactions incur a 0.3% protocol fee. This fee is processed separately as protocol overhead reserves, while the remaining 99.7% of the asset reserves remain permanently locked in the bonding curve pool to back the token value. This mathematical construct guarantees that the circulating supply is always supported by liquid, verifiable reserve assets.

4. Self-Deprecation & Infinite Buyback Phase

When the cumulative net reserves reach $500 \cdot \ln(100) \approx 2,302.585 \text{ ETH}$, exactly 99% of the maximum token supply ($99$ Billion uDOGE) has been minted.

At this juncture, the state flag `mintingPermanentlyDisabled` locks permanently to True. The contract shifts irreversibly into a deflationary buyback black hole: mints are disallowed forever, yet any holder can burn uDOGE at any time to reclaim its proportional backing in ETH from the reserve vault.

5. Game-Theoretic Safeguards (MEV Cooldown)

To shield the protocol from sandwich bots, flashloan exploits, and immediate cornering of initial liquidity:

1. Single-Block Cooldown: Wallets purchasing uDOGE are strictly prohibited from selling within the same transaction block.
2. Per-Transaction Limit: Swap purchases are restricted to a maximum of $5 \text{ ETH}$ per transaction, providing a fair window for decentralized retail accumulation.