🚀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 21 Tn, the remaining $B tokens and collected pegged tokens will migrate to a DEX. Approximately 21 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 = 9,000,000,000
Initial virtual token reserve (iv$B): 1,000,000,000
Initial virtual reserve of Tn (ivTn): 9
Initial price (P(i)): 0.000000009 Tn
P(i)=ivTn/iv$B=9/1,000,000,000=0.000000009
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= 9,000,000,000 / 300,000,000 = 30
Tn = ivTn - vTn = 30 - 9 = 21
Thus, real-time price:
P(700,000,000)=30/(1,000,000,000 - 700,000,000)=0.0000001Tn
Value Overview
Actual Total Supply of $B (S): 888,000,000
Initial Virtual Reserve of $B (iv$B): 1,000,000,000
Reward Pool at Migration (in $B and Tn): 112,000,000
Initial Virtual Reserve of Tn (ivTn): 9
Final Virtual Reserve Threshold (vTn_final): 21
Initial Price of $B (P(i)): 0.000000009 Tn
Final Price of $B (P(final)): 0.0000001 Tn
Market Cap Threshold: 70 Tn (calculated as 0.0000001 × 700,000,000)
At Graduation
Allocated Tokens (A): 700,000,000 $B
Total Tn Raised: 21 Tn
Fees Deducted: 2.2 Tn (after paying third-party service fees; remaining amount goes 100% to the issuer)
Pricing (DEX Initialization)
At the time of migration:
700,000,000 $B tokens were sold pre-migration
Remaining 188,000,000 $B (888,000,000 - 700,000,000) tokens were transferred into the DEX pool
Along with 18.8 Tn, this forms the basis of the initial DEX price
Price Setup
P(Graduation) = vTn(final) / v$B(final)= 18.8 / 188,000,000 = 0.0000001Tn
*The initial DEX pool price is identical to the price at the last moment prior to migration.
Graduation Example
Total Supply (S): 888,000,000
Allocated at Graduation (A): 700,000,000
Total Price-Pegged Tokens Collected at Graduation: 21 Tn (vTn - ivTn = 30 - 9)
Tn Remaining in DEX Pool After Graduation: 21 Tn - 2.2 Tn = 18.8 Tn
Post-Graduation Real-Time Price on DEX: 0.0000004 Tn
Post-Graduation DEX Pool Composition: 188,000,000 tokens + 18.8 Tn
In addition, 12,000,000 $ARToken will be allocated as a reward.
Summary
The total initial supply of $ARToken issued by users is 1,000,000,000 tokens, with an actual circulating supply of 888,000,000 tokens.
The initial virtual pool consists of 0.9 ETH + 1,000,000,000 $ARToken.
A total of 2.1 ETH is raised during the offering, corresponding to a market cap of 7 ETH, with a real-time token price of 0.00000001 ETH. A total of 700,000,000 tokens are purchased by users.
After migration to Uniswap, the on-chain pool contains 1.88 ETH + 188,000,000 $ARToken.
Upon migration, 112,000,000 $ARToken is allocated to the reward pool.
The remaining 0.22 ETH, after covering migration costs, is allocated as a reward to the issuer
Token Metrics
Actual Total Supply of $ARToken: 888,000,000
Initial Virtual Reserve of $ARToken: 1,000,000,000
Reward Pool at Migration: 112,000,000 $ARToken
Initial ETH Virtual Reserve: 0.9 ETH
Critical ETH Reserve Point: 2.1 ETH
Initial Token Price P(i): 0.0000000009 ETH
Final Token Price P(final): 0.00000001 ETH
Market Cap at Critical Point: 7 ETH
Total Supply (S): 888,000,000
Distributed at Graduation (A): 700,000,000
ETH Raised at Graduation: 2.1 ETH
Post-Graduation DEX Pool ETH: 2.1 - 0.22 = 1.88 ETH
Post-Graduation Real-Time DEX Price: 0.00000001 ETH
Post-Graduation DEX Pool Composition: 188,000,000 $ARToken + 1.88 ETH
Remaining 112,000,000 $ARToken allocated to reward poo
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