This mechanism uses a bonding curve with virtual reserves, exponential pricing, and Thirdtrade migration. It covers initial pricing, allocation, fees, and token calculations. The documentation explains PumpMore token operations from launch to migration to the Thirdtrade Dex.
Introduction
This document outlines the implementation of a bonding curve mechanism for buying and selling tokens on PumpMore based on virtual collateral and token reserves, using a Constant Product Model (also known as a Constant k curve).
The curve has an exponential shape so that the price rises slowly at the start and faster towards the end. Once 80% of the 1B token supply is sold on the curve, the Fully Diluted Valuation (FDV) reaches 150,000 AA, and all remaining tokens & collateral migrate to Thirdtrade. Approximately 31,400 AA of collateral is collected on the curve.
Constant Product Model (Constant k)
The core equation of the model is:
k = vTOKEN * vAA
Where:
- k is a constant
- vTOKEN is the virtual token reserve
- vAA is the virtual AA reserve
This constant product is maintained throughout the token sale process, creating the bonding curve.
Initial Values and Calculations
- Total supply of tokens (T) = 1,000,000,000
- Initial virtual token reserve (iVTOKEN) = 1,073,000,000
- Target FDV at ~80% sold = 150,000 AA
- Target price at ~80% sold = 150,000 AA / 1,000,000,000 = 0.00015 AA per token
- Initial price = 0.00001 AA per token (calibrated to reach target)
- Initial virtual AA reserve (iVAA) = 1,073,000,000 * 0.00001 ā 10,730 AA
- Constant k = 1,073,000,000 * 10,730 ā 11,513,290,000
Key Parameters
- Minimum price: 0.00001 AA
- Allocation at Migration (A) = 799,820,983,207,404,442 tokens (with 9 decimals)
- This triggers migration to Thirdtrade
- Maximum allocation of 820,000,000 tokens (82% of total supply) can be sold on the curve if a large trade occurs near the 80% threshold
- FDV at ~80% of tokens sold = 150,000 AA
- Market Cap at ~80% of tokens sold = 120,000 AA
- Migration fees:
- 750 AA paid to Thirdtrade
- 450 AA paid to PumpMore
- Total migration fee = 1,200 AA
Price and Collateral at ~80% Sold
(799,820,983,207,404,442 tokens)
- Tokens remaining in reserve: 1,073,000,000 - 799,820,983,207,404,442 = 273,179,016,792,595,558
- AA reserve at ~80% sold: 273,179,016,792,595,558 * vAA = 11,513,290,000 vAA = 11,513,290,000 / 273,179,016,792,595,558 ā 42,130 AA
- Price at ~80% sold: 42,130 / 273,179,016,792,595,558 ā 0.00015 AA per token
- FDV at ~80% sold: 1,000,000,000 * 0.00015 = 150,000 AA
- Actual market cap at ~80% sold: 799,820,983,207,404,442 * 0.00015 ā 120,000 AA
- Collateral collected: 42,130 - 10,730 = 31,400 AA
Collateral Collection Explanation
The collateral collected is calculated as the difference between the final AA reserve (at ~80% tokens sold) and the initial AA reserve:
Collateral = Final AA reserve - Initial AA reserve
= 42,130 - 10,730 = 31,400 AA
We subtract the initial AA reserve (10,730) because this amount was not actually collected from token sales; it was the initial "virtual" reserve set up to create the bonding curve. The 31,400 AA represents the actual AA collected from token sales.
Explanation of the 10,730 AA subtraction:
The subtraction of 10,730 AA in the collateral calculation is crucial for accurately representing the amount of AA actually collected during the token sale process. Here's a more detailed explanation:
- Initial State: At the start, we set up a "virtual" reserve of 10,730 AA. This isn't real AA that we possess; it's a mathematical construct to create the desired bonding curve shape.
- Final State: At ~80% tokens sold, our AA reserve has grown to 42,130 AA. This includes both our initial virtual reserve and the AA collected from token sales.
- Actual Collateral: To determine how much AA we actually collected, we need to subtract our initial virtual reserve: 42,130 AA (final reserve) - 10,730 AA (initial virtual reserve) = 31,400 AA (actual collateral collected)
This 31,400 AA represents the real AA that has been collected through the token sale process. It's this amount (minus fees) that will be used to provide liquidity on Thirdtrade.
By subtracting the initial virtual reserve, we ensure that we're only counting the AA that was actually collected, not the "virtual" AA that was used to set up the bonding curve initially.
Simulation
Tokens to Migrate (M) Calculation
M = (Collateral collected - Migration fees) / Price at ~80% sold
= (31,400 - 1,200) / 0.00015
ā 192,600,000 tokens
Tokens to Burn (B) Calculation
B = Total Supply - Allocation - Tokens to Migrate
= 1,000,000,000 - 799,820,983,207,404,442 - 192,600,000
ā 7,579,016,792,595,558 tokens
Final State After Migration
- Tokens sold on curve: 799,820,983,207,404,442
- Tokens migrated to Thirdtrade: 192,600,000
- Tokens burned: 7,579,016,792,595,558
- Total tokens in circulation: 992,420,983,207,404,442
- AA collected as collateral: 31,400 AA
- AA used for Thirdtrade liquidity: 31,400 - 1,200 = 30,200 AA
Thirdtrade liquidity pool is created with 30,200 AA and 192,600,000 PumpMore tokens.
Summary
This mechanism ensures:
- A smooth exponential price curve from 0.00001 AA to 0.00015 AA
- Approximately 150,000 AA FDV at ~80% tokens sold
- 120,000 AA market cap at ~80% tokens sold (~$21,600 at current AA price)
- Collection of 31,400 AA as collateral
- Sufficient collateral for migration fees and initial liquidity on Thirdtrade
The Constant k Model provides a predictable and transparent token sale process, incentivizing early participation while ensuring a fair distribution and value accrual for the PumpMore ecosystem.