🚀Bonding Curve

Ultiland ARToken Bonding Curve V2_Mar. 2025

Definition

This is the implementation of a Bonding Curve mechanism for buying and selling Ultiland tokens, based on virtual collateral and token reserves, also known as a constant product curve. The curve has a quadratic shape, causing token prices to increase slowly at first and then rise rapidly toward the end.

Once approximately 700 million $B tokens have been sold through the curve, raising around 84 Tn, the remaining $B tokens and collected pegged tokens will migrate to a DEX. Approximately 84 Tn of pegged tokens will be accumulated on the curve.

T (Token Quantity Base): The reference base for token quantity. Considering Ultiland LaunchPad operates on multiple blockchains with different pegged tokens, an adjustable parameter n (default: 0.1) is introduced, with T multiplied by n (Tn), adapting to each chain. The parameter can be adjusted in real-time based on market developments.

For example, when using ETH as the pegged token, set n = 0.1. Tn represents the funds spent by users to buy tokens.

$ARToken: The generic name for tokens issued by users on Ultiland LaunchPad, abbreviated as $B.

Curve

v$B * vTn = k

Where:

v$B = Virtual reserve of user-issued tokens

vTn = Virtual reserve of pegged tokens

k = Constant determining the shape of the curve, remaining unchanged

(analogous to the AMM algorithm x × y = k)

Setting Initial Values

Coefficient k is set based on the initial token price:

k= iv$B*ivIn = 36,000,000,000

Initial virtual token reserve (iv$B): 1,000,000,000

Initial virtual reserve of Tn (ivTn): 36

Initial price (P(i)): 0.000000036 Tn

P(i)=ivTn/iv$B=36/1,000,000,000=0.000000036

Real-time Price Calculation

The real-time price is calculated using the remaining $B and the vTn reserve via the constant product formula:

P(Q) = vTn/v$B

v$B = iv$B-Q, v$B≤iv$B

vTn= ivTn+ Tn, vTn ≥ivTn

P(Q): Price at token quantity Q

v$B: Current virtual reserve, calculated as initial virtual token reserve minus tokens sold. When users buy $B, v$B decreases and vTn increases; when users sell $B, v$B increases and vTn decreases.

Example: When users buy 700 million $B tokens:

v$B = iv$B-Q=1,000,000,000- 700,000,000 =300,000,000

vTn = k/v$B=36,000,000,000/300,000,000 = 120

Tn = ivTn -vTn = 120 -36 = 84

Thus, real-time price:

P(700,000,000)=120/(1,000,000,000 - 700,000,000)=0.0000004Tn

Token Metrics

• Actual total supply of $B (S): 888,000,000

• Initial virtual reserve (iv$B): 1,000,000,000

• Tokens to be burned during migration: 112,000,000

• Initial virtual reserve of Tn (ivTn): 36

• Final virtual reserve threshold (vTn_final): 84

• Initial price (P(i)): 0.000000036 Tn

• Threshold price (P(final)): 0.0000004 Tn

• Market cap threshold: 280 Tn (0.0000004 × 700,000,000)

Migration to DEX

• Allocated tokens (A): 700,000,000

• Total raised Tn: 84 Tn

• Fees deducted: 8.8 Tn

(After third-party fees, 90% to issuer, 5% for ARTX buyback & burn, 5% as platform revenue. If ARTX is not issued yet, funds for ARTX burn accumulate until ARTX launch.)

Price at Migration

At migration, remaining 188,000,000 tokens (888M – 700M) and 75.2 Tn will move to the DEX liquidity pool, establishing the initial DEX price.

P(Migration)=vTn(final)/v$B(final)=75.2/188,000,000=0.0000004Tn

*The initial DEX pool price is identical to the price at the last moment prior to migration.

Tokens Burned at Migration

At migration, the remaining 112,000,000 virtual tokens (iv$B, 1,000,000,000 - 888,000,000) are burned, ensuring the actual token issuance and circulating supply meet the set parameters.

Migration Example

• Total Supply (S): 888,000,000

• Allocated Tokens at Migration (A): 700,000,000

• Pegged Tokens Collected at Migration: 84 Tn (vTn - ivTn = 120 - 36)

• Pegged Tokens Transferred to DEX Pool: 75.2 Tn (84 Tn - 8.8 Tn)

• Real-time Price at DEX Pool Migration: 0.0000004 Tn

• Post-migration DEX Pool:

• 188,000,000 $ARToken + 75.2 Tn

• Tokens Burned: 112,000,000 $ARToken

Notes on Fees at DEX Migration

DEX migration fees include:

1. Ultiland migration expenses (smart contract audit costs, migration gas fees).

2. Fees charged by certain DEX platforms (e.g., Solana chain: 1 SOL fee for Raydium, 3 SOL fee for Openbook).

Any remaining unspent Tn funds after fee deductions will be used to repurchase the Ultiland platform token ($ARTX):

• 5% burned

• 5% allocated as Ultiland revenue

• 90% evenly distributed among $ARToken issuers

If $ARTX has not yet been launched, the 5% burn allocation accumulates in the treasury until $ARTX is issued. The remaining 95% (issuer revenue and platform income) is distributed in the pegged tokens.

Final Summary (ETH Example)

1. Initial issued $ARToken total supply: 1,000,000,000; actual supply after adjustment: 888,000,000

2. Initial virtual liquidity pool: 3.6 ETH + 1,000,000,000 $ARToken

3. Total funds raised: 8.4 ETH, corresponding market cap: 28 ETH; real-time token price: 0.00000004 ETH, total minted: 700,000,000 tokens

4. Post-migration Uniswap pool: 7.52 ETH + 188,000,000 $ARToken

5. Tokens burned at migration: 112,000,000

6. Remaining funds (0.88 ETH) after paying migration fees will be redistributed:

• 5%*0.88 ETH burned

• 5%*0.88 ETH to Ultiland

• 90%*0.88 ETH evenly distributed to $ARToken issuers

(If $ARTX is not yet issued, the 5% burn funds accumulate in the treasury until $ARTX launch. The remaining 95% is distributed in ETH.)

Metric Amount

• Actual total supply of $ARToken: 888,000,000 tokens

• Initial virtual reserve of $ARToken: 1,000,000,000 tokens

• $ARToken tokens to be burned at migration: 112,000,000 tokens

• Initial virtual ETH reserve: 3.6 ETH

• Final virtual ETH reserve threshold: 8.4 ETH

• Initial $ARToken price (P(i)): 0.0000000036 ETH

• Final threshold price of $ARToken (P(final)): 0.00000004 ETH

• Market cap at final threshold: 28 ETH

• Total supply (S): 888,000,000 tokens

• Allocated tokens at migration (A): 700,000,000 tokens

• ETH collected at migration: 8.4 ETH

• ETH transferred to DEX Pool: 7.52 ETH (8.4 ETH - 0.88 ETH fees)

• Real-time DEX Pool price at migration: 0.00000004 ETH

After migration, 188,000,000 tokens and 7.52 ETH will be placed into the DEX pool, and 112,000,000 $ARToken tokens will be permanently burned.