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.

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 14,000 XPAA, and all remaining tokens & collateral migrate to Thirdtrade. Approximately 2,925 XPAA of collateral is collected on the curve.

Constant Product Model (Constant k)

The core equation of the model is:

k = vTOKEN * vXPAA

Where:

k is a constant

vTOKEN is the virtual token reserve

vXPAA is the virtual XPAA 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 = 14,000 XPAA

Target price at 80% sold = 14,000 XPAA / 1,000,000,000 = 0.000014 XPAA per token

Initial price = 0.00000093 XPAA per token (calibrated to reach target)

Initial virtual XPAA reserve (iVXPAA) = 1,073,000,000 * 0.00000093 ≈ 998 XPAA

Constant k = 1,073,000,000 * 998 = 1,070,854,000

Key Parameters

Minimum price: 0.00000093 XPAA

Allocation at Migration (A) = 80% of total supply = 800,000,000

This triggers migration to Thirdtrade
Maximum allocation of 82% can be sold on the curve if a large trade occurs near the 80% threshold

FDV (Fully diluted valuation) at 80% of tokens sold = 14,000 XPAA

Market Cap at 80% of tokens sold = 11,200 XPAA

Migration fees:

224 XPAA paid to Thirdtrade
100 XPAA paid to PumpMore
Total migration fee = 324 XPAA

Price and Collateral at 80% Sold (800,000,000 tokens)

Tokens remaining in reserve: 1,073,000,000 - 800,000,000 = 273,000,000

XPAA reserve at 80% sold: 273,000,000 * vXPAA = 1,070,854,000 vXPAA = 1,070,854,000 / 273,000,000 ≈ 3,923 XPAA

Price at 80% sold: 3,923 / 273,000,000 ≈ 0.000014 XPAA per token

FDV at 80% sold: 1,000,000,000 * 0.000014 = 14,000 XPAA

Actual market cap at 80% sold: 800,000,000 * 0.000014 = 11,200 XPAA

Collateral collected: 3,923 - 998 = 2,925 XPAA

Collateral Collection Explanation

The collateral collected is calculated as the difference between the final XPAA reserve (at 80% tokens sold) and the initial XPAA reserve:

Collateral = Final XPAA reserve - Initial XPAA reserve = 3,923 - 998 = 2,925 XPAA

We subtract the initial XPAA reserve (998) because this amount was not actually collected from token sales; it was the initial "virtual" reserve set up to create the bonding curve. The 2,925 XPAA represents the actual XPAA collected from token sales.

Explanation of the 998 XPAA subtraction:

The subtraction of 998 XPAA in the collateral calculation is crucial for accurately representing the amount of XPAA 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 998 XPAA. This isn't real XPAA that we possess; it's a mathematical construct to create the desired bonding curve shape.

Final State: At 80% tokens sold, our XPAA reserve has grown to 3,923 XPAA. This includes both our initial virtual reserve and the XPAA collected from token sales.

Actual Collateral: To determine how much XPAA we actually collected, we need to subtract our initial virtual reserve: 3,923 XPAA (final reserve) - 998 XPAA (initial virtual reserve) = 2,925 XPAA (actual collateral collected)

This 2,925 XPAA represents the real XPAA 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 XPAA that was actually collected, not the "virtual" XPAA 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 = (2,925 - 324) / 0.000014 ≈ 185,785,714 tokens

Tokens to Burn (B) Calculation

B = Total Supply - Allocation - Tokens to Migrate = 1,000,000,000 - 800,000,000 - 185,785,714 = 14,214,286 tokens

Final State After Migration

Tokens sold on curve: 800,000,000

Tokens migrated to Thirdtrade: 185,785,714

Tokens burned: 14,214,286

Total tokens in circulation: 985,785,714

XPAA collected as collateral: 2,925 XPAA

XPAA used for Thirdtrade liquidity: 2,925 - 324 = 2,601 XPAA

Thirdtrade liquidity pool is created with 2,601 XPAA and 185,785,714 PumpMore tokens.

Summary

This mechanism ensures:

A smooth exponential price curve from 0.00000093 XPAA to 0.000014 XPAA

Exactly 14,000 XPAA FDV at 80% tokens sold

11,200 XPAA market cap at 80% tokens sold

Collection of 2,925 XPAA as collateral, close to the target of ~2,857 XPAA

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.

Bonding Curve