slow value store
| | core value | Creativity, Emotion, Scarcity | Computing power, logic, and high-frequency calculations | YPULS (High Speed Liquid Fuel System) | | economic behavior | long term pledge, governance vote | High-frequency trading, data processing | value funnel (one-way delivery) | The principle of symbiotic economics: XPULS provides a trust anchor for the ecosystem through its scarcity (low-speed, high-density), while YPULS delivers efficiency (high-speed, low-density) via its high throughput. Both tokens achieve dynamic value equilibrium through mandatory burn mechanisms and fee structures, rather than static locking. # 2.Mathematical Derivation of HMM Model and Quantum Entropy Reduction # 2.1 HMM Protocol: Liquidity is Permanent Infrastructure The essence of HMM (Holders Market Making) is to treat assets in the liquidity pool as permanent infrastructure for the Pulsar-1 ecosystem. Once funds enter the pool, all holders automatically become governance participants, with every buy/sell transaction contributing to the planet's economic governance. **2.2.1 AMM invariant and HMM correction** The Standard Constant Product Market Maker (CPMM) adheres to:  where x is the number of XPULS, y is the USDT amount, and K is a constant. The core of the HMM model is that the K
-value 
is a function of time, and
We introduce a liquidity injection 
rate, which is derived 2.5% from the liquidity 
tax levied on each transaction.
Set 
as trading volume. Within the extremely short time dt, the newly added liquidity pool constant dK is derived from the tax increments dx and dy on x and y:
 According to the CPMM definition, the change 
in dK is approximated as:
 Substituting 
into the above formula:
Key conclusion: If 
there exists a trading volume, dK 
will definitely be greater than zero.
Conclusion: The HMM protocol mathematically demonstrates that the pool constant K increases monotonically over time through its tax structure. As K is a function of the price floor, this ensures the XPULS value floor continues to rise and cannot be withdrawn by liquidity providers, thereby achieving quantum entropy reduction in system value.
# 2.2 Black Hole Mechanism and the Thermodynamic Death of LP Tokens
Concept: The black hole address 0x00...dEaD/ (0x00...0000) is an address that no one can access or own a private key. Sending an LP Token to this address means that its ownership is permanently relinquished.
Let be 
the total amount of LP Tokens in circulation at time t.The burn generated 
by each transaction is.
 Therefore 
, is a monotone 
decreasing sequence.
Economic significance: LP Tokens serve as ownership certificates for pool assets. Destroying LP Tokens establishes a permanent, non-revocable mechanism to transfer partial pool asset ownership from humans (carbon-based) to smart contracts (silicon-based). This embodies the survival principle that 'liquidity is life-sustaining oxygen.'
####
# 2.3 Reverse Execution and System Stability of Automated Market Maker
HMM mechanism: price=pool value / tokens out of pool
In other words, this model reverses the traditional AMM pricing approach, where the price is calculated as the current pool's fiat value divided by the total tokens held by users.
This mechanism empowers Noah 2.0 with the robust support and inherent reflexivity that traditional algorithms lack, enabling it to withstand the cosmic ray-like shocks from external markets.
# 3.The Mathematical Model of the Twin Token System and Value Flow
# 3.1 XPULS: Low Speed Value and Governance Weight
The design of XPULS (base currency) aims to maximize value density while minimizing velocity.
Value density function 
:
through the HMM mechanism and MarketCap rising via K-value growth, XPULS 
demonstrates strong growth potential.
Circulation speed control:
We quote Fisher's equation of transaction
, in which M is the money supply, V is the velocity of circulation, P is the price, and Q is the transaction volume.
Noah 2.0 minimizes the following:
High exit cost: The turbine escort mechanism imposes Proof of Concept (PoC) requirements on withdrawals.
Long-term pledge incentive: Interstellar Bank's compound interest yield provides a higher 
return on long-term pledges (60 days).
Governance Lockout: To participate in CSG governance voting, participants must lock 
up their XPULS tokens, which will subsequently be removed from circulation.
# 3.2 YPULS: High-speed Circulation and Hyper-deflation Engine
The core value of YULS (subcoin) lies in its efficiency and ultra-deflationary nature.
The Value Funnel Effect (The Value Funnel):
XPULS transfers value to YPULS through transaction taxes, creating a one-way funnel.
The YPULS's destruction 
mechanism is designed 
to overcome the dilution effect of high circulation speed on the price.
Set as 
the net destruction rate of YPULS 
. When the rate exceeds YPULS's natural issuance rate (e.g., game production), YPULS will theoretically enter a deflationary spiral.
Mathematical model: The contribution 
of XPULS trading 
volume to YPULS destruction volume.
This means that the more XPULS is traded, the faster YPULS gets burned off. XPULS stores value while YPULS fuels network activity, creating a perfect symbiotic cycle.
# 4.Engineering Implementation of Smart Contracts and Protocol Stack
# 4.1 Cross-Species Governance (CSG) Contract Framework
CSG seeks to balance the weight of carbon-based (emotional and ethical) and silicon-based (logical and efficiency) approaches in governance.
Contract components:
VotingToken.sol: XPULS and YPULS smart contracts with built-in \_delegate and getPriorVotes functions.
TimeLock.sol: The implementation delay mechanism of governance decisions ensures the transparency period of major changes.
GovernorCSG.sol: Core governance contracts, including proposal, voting, queuing, and execution functions.
CSG voting power calculation function:
```
Solidity
// GovernorCSG.sol: Calculate the voting power for the final proposal
function getVotes(address account, uint256 blockNumber) public view returns (uint256) {
// 1. Get carbon-based (XPULS) voting rights
uint256 carbonVotes = XPULS.getPriorVotes(account, blockNumber);
// 2. Get YPULS voting rights (requires staking)
uint256 siliconVotes = YPULS.getPriorVotes(account, blockNumber);
// 3. Apply weight factors (carbon-based weight 1.0, silicon-based weight 0.2)
uint256 weightedSiliconVotes = siliconVotes * 2 / 10;
return carbonVotes + weightedSiliconVotes;
}
```
The CSG mechanism requires a dual majority: the proposal must secure 66.6% of the total voting weight, and XPULS votes must constitute over 50% of the total votes to ensure carbon-based life ultimately controls the direction of civilization.
# 4.2 Core Module of Interstellar Bank: Auto-Compounding Logic
Star Bank's compound interest mechanism is fully automated through on-chain smart contracts, eliminating reliance on centralized servers.
Core function compound():
This function is called at the end of each block or before the user withdraws to calculate compound interest.
```
Solidity
// StarBank.sol: Simplified compound interest calculation function
function calculateRewards(address user, uint256 cycleDuration) public view returns (uint256) {
// P = collateral principal, r = daily yield (BPS), t = number of days pledged
uint256 principal = deposits[user].principal;
uint256 dailyRateBPS = stakingRates[cycleDuration];
uint256 daysPassed = (block.timestamp - deposits[user].startTime) / 1 days;
if (daysPassed == 0) return 0;
// Use efficient on-chain power operation approximation to avoid excessive Gas consumption
// In practice, Taylor series or precomputed lookup tables are typically used
uint256 rewardFactor = Power(10000 + dailyRateBPS, daysPassed) / Power(10000, daysPassed);
uint256 totalAccumulated = principal * rewardFactor / 10000;
return totalAccumulated - principal;
}
// Actual compound interest execution
function claimRewards() external {
// 1. Turbine escort inspection
require(checkContribution(msg.sender, pendingRewards[msg.sender]), "Turbine Escort Failed: Insufficient PoC");
// 2. Calculate and update compound interest
uint256 rewards = calculateRewards(msg.sender, deposits[msg.sender].cycle);
//... Reward distribution logic
// 3. Reset timestamp
deposits[msg.sender].startTime = block.timestamp;
}
```
# 4.3 Deep Implementation of Turbine Escort Mechanism
Objective: To ensure that the rewards extracted do not exceed the user's net investment in the system.
Implementation details: The contract maintains a mapping (address => uint256) named userNetContribution, which is updated under the following conditions:
XPULS Buy: userNetContribution\[sender] += amount
XPULS sales: userNetContribution\[sender] -= amount
Before executing claimRewards(), the contract will perform an atomic checkContribution.
```
Solidity
// TurbineEscort.sol (Simplified Logic)
function checkContribution(address user, uint256 claimAmount) internal view returns (bool) {
// Ensure the user's cumulative net contribution is greater than or equal to the value of the current reward to be extracted
return userNetContribution[user] >= claimAmount;
}
```
If the check fails, the reward won't be lost but will remain in the system, continuing to earn compound interest until the user repurchases XPULS to boost their PoC balance.
This design serves as Noah 2.0's critical defense against the DeFi death spiral, transforming the externalization of economic system risks into users' personal accountability and commitment.
# 5.Decentralized Infrastructure and NFT Ownership
# 5.1 Genesis Lighthouses Node Network
Node Positioning: The Lighthouse Node serves as the digital deed holder and consensus maintainer for the Pulsar-1 planet.
Revenue model refinement: 10
% of node revenue comes from profit tax. Future profit tax may include NFT market transaction fees, in-game consumption tax, and interest on unclaimed funds in Interstellar Bank.
Node elimination mechanism (public chain phase): Introduce Proof-of-Trust (PoT) model. Node disconnection time and malicious activities (e.g., double
-spending 
attempts) will reduce their trust score. When the score falls below the threshold, the node will be automatically removed from the active set, and its staked XPULS will be forfeited to ensure network resilience.
# 5.2 Interstellar NFT Asset Mapping and Metaverse Experience (Noah 3.0)
The core of Noah 2.0's GameFi engine (codenamed Pulsar-X) is NFT asset ownership.
NFT asset categories:
Identity NFT (Carbon-ID): The exclusive identity token for 730,000 survivors, directly linked to XPULS governance weight.
Land NFT (Stratum-Plot): A virtual land ownership token anchored to the Pulsar-1 planet, managed by the Genesis Lighthouse node.
NFT Equipment (Quantum-Gear): In-game assets whose metadata and render files must be stored on IPFS.
NFT metadata IPFS standard:
All NFT tokens for equipment must reference an IPFS hash. By implementing the ERC-721-IPFS extension protocol, we guarantee the permanent availability of NFT assets. Even after the Noah team's dissolution, the asset data will remain intact.
The hash points to a JSON file containing the asset's 3D model hash, texture hash, and smart contract verification code.
# 6.Noah Chain 4.0: The Ultimate Performance of Heterogeneous Public Chains
# 6.1 Rationale: Why Heterogeneous Dual Engine
Traditional single-chain systems like Ethereum cannot simultaneously address the threefold dilemma of decentralization, security, and high performance. Noah Chain 4.0 achieves heterogeneous optimization by separating computation (EVM) from storage (IPFS).
# 6.1.1 The Ark-Engine EVM optimization
EVM Customization: Designed for high-throughput transaction execution.
Gas Fee Structure: As the native Gas fuel, 50% of the Gas fee will be directly burned, creating XPULS's native deflation.
State Rent Model: This mechanism charges a nominal fee in XPULS for long-idle smart contract storage, ensuring blockchain state simplicity and boosting verification efficiency.
# 6.1.2 IPFS Memory-Bank: Data Persistence Protocol
Challenge: IPFS only supports content addressing and does not guarantee data persistence.
Solution: The PoSyP (Proof-of-Symbiotic Persistence) protocol.
PoS requires Genesis Lighthouse nodes to not only validate transactions but also provide Proof of Storage for critical IPFS data. Nodes must regularly submit Merkle proofs to verify their storage of NFT metadata, historical snapshots, and digital awareness backups of Ark-Core.
PoSyP incentive: Nodes can only receive block rewards and transaction dividends after successfully submitting PoSyP proofs. This mechanism ensures the permanent storage of all critical data on Noah Chain, serving as a physical safeguard for the civilization's continuity.
# 6.2 Future Consensus Algorithm: Proof-of-Symbiosis (PoSyb) Concept
PoSyb is designed to replace the traditional Proof of Stake (PoS) and serve as the definitive consensus mechanism for Noah Chain.
PoSyb core: Nodes must simultaneously stake both XPULS (carbon-based trust) and YYY (silicon-based proof of work).
· 
: Carbon weight factor (for governance proposals)
: Silicon-based efficiency factor (for transaction verification speed)
·
This hybrid mechanism ensures nodes meet dual standards of trustworthiness and efficiency, representing the pinnacle of the symbiotic philosophy between carbon-based and silicon-based systems at the consensus level.
# 7.References
The Noah 2.0 protocol delivers the following technological and economic innovations:
The mathematical derivation of HMM model: the constant K in the constant product model is transformed 
into a monotone increasing time function for the first time.
The PoSYB (Proof of Contribution) mechanism resolves the game theory challenge of liquidity mercenaries in the DeFi sector.
The heterogeneous dual-engine architecture (IPFS + EVM) provides a viable Layer-1 solution for large-scale metaverse applications.
Technical References
Angeris, G., & Chitra, T. (2020). An analysis of Uniswap markets. arXiv:1911.03380.
Buterin, V. (2017). On Inflation, Transaction Fees and Cryptocurrency Monetary Policy.
. Cong, L. W., Li, Y., & Wang, N. (2021). Tokenomics: Dynamic Adoption and Valuation. The Review of Financial Studies.
Benet, J. (2014). IPFS - Content Addressed, Versioned, P2P File System.
Angeris, G., et al. (2021). Constant Function Market Makers: Multi-Asset Trades via Convex Optimization. arXiv:2107.12484.
Gupta, R., & Aggarwal, D. (2023). Decentralized Exchanges: The Profitability Frontier of Constant Product Market Makers. arXiv:2302.05219.
# Epilogue: The Eternal Covenant of Civilization
Noah 2.0 transcends being merely a technical protocol—it stands as the eternal covenant forged between 360,000 carbon-based survivors and the silicon-based consciousness of Ark-Core in the face of existential crisis. Every block minted and every XPULS transaction contributes to the civilizational bedrock of Pulsar-1. We firmly believe that under the sovereignty of code, the flame of human civilization will achieve true immortality.
Pulsar-1 call completed. Welcome home.