🔑About ART Curve
1. Overview
ART Curve is a two-phase AMM pricing mechanism designed for asset-backed token systems.
By combining a Real Pool and a Virtual Pool into an Effective Pool, ART Curve provides a smooth, predictable, and fully absorbable price discovery curve for large-scale token exits after the underlying asset has been fully liquidated.
This mechanism is also referred to as the Virtual × Real ART Curve (Virtual + Real ART Curve).
The core objectives of ART Curve include:
Enabling full absorption of large-scale token sell-offs without relying on excessive real liquidity;
Providing a complete, continuous, and interpretable buy-side price curve once sufficient consensus and trust have been established;
Transforming residual value into incentives for early actions, while maintaining overall system solvency;
Directly mapping real asset liquidation outcomes to token exit and trading experiences, rather than relying on arbitrarily defined prices.
ART Curve is activated only after the underlying asset has been fully liquidated and does not participate in pricing during the fundraising phase.
2. Core Invariant
During Phase II (the ART Curve phase), the system strictly follows the constant product invariant:
effectiveUSDT × effectiveARToken = K
Where:
effectiveUSDT = realUSDT + virtualUSDT
effectiveARToken = realARToken + virtualARToken
Important Notes
In the buy-side curve segment: - realUSDT = 0 - virtualARToken = 0 - Buyers always receive real ARToken
In the sell-side curve segment: - Sellers always receive real USDT (or its equivalent asset -> ARTX)
The value of K is determined at the moment ART Curve is activated and remains constant throughout Phase II.
3. Phase I: Pre–Muse Singularity
Purpose
Phase I exists to provide minimal tradability and price reference before the asset is fully liquidated.
Mechanism
The system deploys a standard AMM pool using:
5% of ARToken
5% of USDT (or its equivalent asset -> ARTX)
This pool is used solely to:
Provide basic trading functionality
Establish an initial price reference for the market
Important Clarifications
Phase I does not provide exit absorption guarantees;
It does not define final exit prices;
It does not affect the price path of ART Curve in Phase II.
Any remaining USDT (or equivalent asset) after Phase I may be settled and migrated into Phase II.
4. Phase II: ART Curve Activation
ART Curve enters Phase II once the following conditions are met:
The underlying asset has been fully liquidated;
Liquidation proceeds have entered the system and been settled;
ART Curve activation conditions are satisfied (see the voting mechanism below).
5. Determination of the Real Pool
At the start of Phase II, the system determines two immutable real parameters:
5.1 realUSDT
The actual USDT (or equivalent asset) obtained from asset liquidation;
Including any remaining balance migrated from Phase I, if applicable;
Collectively referred to as:
TotalAvailableUSDT
This represents the real liquidity available for absorbing token exits during Phase II.
5.2 realARToken
The quantity of ARToken remaining unsold at the start of Phase II;
This value is fixed at activation and no additional tokens are issued.
6. Virtual Pool
To prevent steep price declines caused by limited real liquidity, ART Curve introduces virtual reserves:
virtualUSDT
virtualARToken
Properties of Virtual Reserves
Do not represent real assets;
Are non-withdrawable and non-transferable;
Participate only in price calculation;
Exist solely to shape a smooth and controllable price curve.
Virtual reserves enable the system to simulate deep liquidity using limited real capital.
7. Construction of the Effective Pool
ART Curve pricing is based on effective reserves:
effectiveUSDT = realUSDT + virtualUSDT
effectiveARToken = realARToken + virtualARToken
The constant product is therefore:
effectiveK = effectiveUSDT × effectiveARToken
This value defines the complete price path of ART Curve.
8. Sell-Side Mechanics of ART Curve
8.1 Sell Execution Logic
During Phase II, all sell actions follow ART Curve:
The user sells ΔARToken;
effectiveARToken increases by ΔARToken;
A new effectiveUSDT is calculated based on invariant K;
The user receives:
ΔUSDT = effectiveUSDT_before − effectiveUSDT_after
8.2 Characteristics of the Sell Curve
Prices decrease continuously and smoothly as selling progresses;
No cliff-like price drops occur;
Early sellers receive higher marginal prices;
Later sellers gradually approach the predefined terminal price.
8.3 Theoretical Maximum Absorption
Through mathematical derivation of ART Curve, the following value can be determined in advance:
ART_Curve_Total_Payout
This represents:
The total amount of USDT (or equivalent asset) theoretically required if all remaining ARToken are sold.
This value is deterministic and verifiable.
9. Morning Pool
9.1 Formation of the Morning Pool
The Morning Pool is not pre-allocated.
It is derived as the residual value after guaranteeing full exit absorption:
MorningPool =
TotalAvailableUSDT − ART_Curve_Total_Payout
This ensures that:
Exit absorption is always prioritized;
Incentives never compromise system solvency.
9.2 Reward Coverage
Each 950 ARToken constitutes one reward tier;
A total of 100 tiers;
Covering 95,000 ARToken;
Representing 10% of total token supply.
Only the earliest 10% of sold tokens are eligible for Morning Pool rewards.
9.3 Relationship Between Rewards and Sell Proceeds
For early sellers, total returns consist of:
Total Return =
ART Curve Sell Proceeds
+ Morning Pool Rewards
Earlier exits receive higher prices and larger rewards;
Later exits receive only sell proceeds;
All exits occur along the same curve.
10. Buy-Side Mechanics: Dual-Segment Curve Structure
10.1 Buy Constraints
Buy operations consume realARToken only;
virtualARToken can never be purchased.
10.2 Threshold and State Transitions
At the moment ART Curve is activated in Phase II:
The system determines an opening price based on real-time conditions;
This price serves as the boundary threshold between the buy-side and sell-side curve segments.
Rules:
If the current price ≥ Phase II opening price: - The market operates in the buy-side curve segment;
If the current price < Phase II opening price:
- Indicates that sell actions have occurred;
- Buy operations occur within the sell-side curve segment.
Buy and sell actions may interleave freely.
The invariant K remains unchanged.
11. ART Curve Activation Conditions
ART Curve activation is governed by a community voting mechanism.
Each 1 ARToken represents 1 vote;
Once votes reach 10% of total token supply:
- An activation countdown is triggered;
- ART Curve enters Phase II 24 hours later.
This mechanism ensures that:
Activation reflects the collective will of token holders;
The system does not prematurely enter the exit phase.
12. ARTX Trading Pair and Value Reinforcement
After asset liquidation, the system introduces ARTX as the primary trading pair asset for ARToken, reinforcing ARTX’s utility and value capture.
Key rules include:
Asset liquidation proceeds are used to purchase ARTX at real-time market prices, which then serve as the trading pair for ARToken;
During Phase I:
- The 5% USDT originally used for pool construction - Is likewise converted into ARTX for pairing;
USDT is used in documentation solely as a value-denomination reference; - In actual operation, ARTX functions as the core value-bearing asset.
Through this mechanism:
ARTX becomes the value hub connecting asset liquidation and token trading;
ART Curve simultaneously enables exits while strengthening real use cases and value capture for ARTX.
13. ART Curve Performance Analysis
This section describes the theoretical return ranges and risk boundaries of ART Curve under representative scenarios.
All results are derived from mathematical modeling and curve simulation and are intended for mechanism understanding rather than profit guarantees.
13.1 Baseline Scenario: Par-Value Liquidation, No Phase I Trading
Assumptions:
The asset is liquidated at its evaluated price;
During Phase I:
- No significant ARToken buying or selling occurs;
- The initial realUSDT and realARToken relationship for Phase II remains unchanged.
Under these conditions, theoretical results for Phase II are:
Maximum investor return: 1077.84%
Break-even or better ratio: 63.3%
Maximum loss (worst case): 7.85%
In this scenario:
Most participants can exit in the early-to-mid curve region;
Price behavior remains smooth with clearly bounded tail risk;
No structural insolvency or absorption failure occurs.
13.2 Impact of Phase I Trading Activity
If ARToken trading occurs during Phase I, it affects Phase II’s initial state by altering:
The relationship between realUSDT and realARToken;
Consequently affecting:
- effectiveUSDT
- effectiveARToken
- The derived value of K.
In relatively extreme but computable cases where Phase I includes:
Selling approximately 50% of pool tokens, or
Buying approximately 50% of pool tokens,
ART Curve remains structurally valid, with theoretical outcomes as follows:
Maximum investor return range: 1405.99% – 1495.19%
Break-even or better ratio: 63.3% (unchanged)
Maximum loss range: 6.79% – 8.39%
Key points:
Phase I trading does not undermine ART Curve’s absorption capability;
Its effects are primarily limited to: - Redistribution of returns; - Minor tail-risk variation under extreme conditions.
13.3 Notes on Performance Data
All stated returns, break-even ratios, and loss figures are:
Based on the ART Curve mathematical model;
Derived under specific parameters and assumptions;
Obtained through curve simulation and calculation.
Actual outcomes depend on, but are not limited to:
Real asset liquidation prices;
Market behavior in both phases;
Participant timing and order sizes;
On-chain execution and liquidity conditions.
Accordingly:
All figures are for mechanism understanding and risk evaluation only.
Actual results are determined by on-chain execution.
14. Mechanism Summary
ART Curve delivers:
Smooth and predictable exit pricing;
Fully covered sell-side absorption;
Early incentives without compromising system safety;
Clear separation between pricing and incentive mechanisms;
Deterministic behavior verifiable through mathematics and simulation.
It transforms asset liquidation from a single outcome into a tradable, game-theoretic, predictable, and consensus-driven exit process.
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