Technical Overview

Architecture Overview

PizzaFun's technical foundation is built on the CrustNet high-speed trading engine, employing a multi-layered architectural design that ensures high performance, security, and scalability. The system architecture comprises four main layers: access layer, business logic layer, consensus layer, and storage layer, forming a complete technology stack.

┌───────────────────────────────────┐
│            Access Layer (L1)      │
│  REST API, WebSockets, GraphQL    │
├───────────────────────────────────┤
│        Business Logic Layer (L2)  │
│ Transaction Processing, Order Matching, Asset Management, Validation │
├───────────────────────────────────┤
│           Consensus Layer (L3)    │
│   Sharded DAG, Hybrid Consensus Algorithm, TSS    │
├───────────────────────────────────┤
│           Storage Layer (L4)      │
│    Distributed Ledger, State Database, IPFS   │
└───────────────────────────────────┘

The system design employs sharding technology and Directed Acyclic Graph (DAG) data structures, allowing simultaneous processing of multiple transaction paths, significantly improving transaction throughput. Experimental data shows that under standard testing environments, CrustNet can achieve peak processing capacity of 35,000 transactions per second (TPS), far exceeding the traditional Bitcoin network's 7 transactions per second.

CrustNet Consensus Mechanism

CrustNet employs an innovative hybrid consensus algorithm—Proof of Velocity (PoV)—combining the advantages of Proof of Stake (PoS) and Verifiable Random Functions (VRF), significantly improving confirmation speed while maintaining security. The consensus process can be expressed through the following mathematical model:

Bnext=argmaxB∈B{vB⋅SB⋅(1−α⋅LB)β}B_{next} = \text{argmax}_{B \in \mathcal{B}} \{v_B \cdot S_B \cdot (1-\alpha\cdot L_B)^{\beta}\}

Where:

  • $B_{next}$ is the next block to be selected

  • $v_B$ is the validator node's velocity coefficient, inversely proportional to historical response time

  • $S_B$ is the validator node's stake value

  • $L_B$ is the validator node's load factor

  • $\alpha$ and $\beta$ are system parameters used to balance speed and decentralization

This consensus mechanism allows the network to achieve 2-second block confirmation times while maintaining strong consistency. Validator selection uses a probabilistic rotation mechanism, ensuring stable block generation times even under high load conditions while preventing centralization risks from stake concentration.

Transaction Processing and Execution

PizzaFun's transaction processing pipeline employs a multi-stage parallel processing architecture, maximizing throughput through transaction decomposition and parallel execution. The transaction execution flow is as follows:

  1. Transaction Reception and Validation: Ensures transaction validity through signature verification, format checking, and double-spend protection

  2. Shard Routing: Allocates transactions to optimal execution paths based on intelligent sharding algorithms

  3. Parallel Execution: Utilizes conflict-free transaction matrices to identify parallelizable transaction sets

  4. State Updates: Atomically updates global state, ensuring consistency

  5. Result Broadcasting: Distributes transaction confirmations through efficient P2P networks

Parallel execution capability can be quantified through the following formula:

Peff=11−p+pn⋅11+α⋅CcommP_{eff} = \frac{1}{1 - p + \frac{p}{n}} \cdot \frac{1}{1 + \alpha \cdot C_{comm}}

Where:

  • $P_{eff}$ is effective parallelism

  • $p$ is the proportion of parallelizable transactions

  • $n$ is the number of validator nodes

  • $C_{comm}$ is communication overhead

  • $\alpha$ is a network topology-related coefficient

The system employs a special conflict detection matrix, representing potential transaction dependencies as directed graphs, and uses graph coloring algorithms to identify parallelizable transaction groups, significantly improving processing efficiency.

Dual-Phase Pricing Mechanism

PizzaFun's dual-phase trading mechanism—Baking Phase and Serving Phase—provides flexible token price discovery and liquidity management solutions. These two phases use different mathematical models:

Baking Phase: Dynamic Price Growth Model

In the baking phase, prices follow an exponential growth curve, expressed as:

P(n)=P0⋅ek⋅nP(n) = P_0 \cdot e^{k\cdot n}

Where:

  • $P(n)$ is the price of purchasing the nth token

  • $P_0$ is the initial price

  • $k$ is the growth coefficient, typically set between 0.0025 and 0.01

  • $n$ is the number of tokens sold

As more tokens are purchased, prices rise exponentially, providing potential appreciation opportunities for early participants.

Serving Phase: Automated Market Maker (AMM) Model

When tokens enter the serving phase, the pricing mechanism transitions to a constant product automated market maker model:

x⋅y=kx \cdot y = k

Where:

  • $x$ is the number of tokens in the token pool

  • $y$ is the amount of Bitcoin in the token pool

  • $k$ is a constant (liquidity parameter)

Trading prices in this phase are determined by the following formula:

P=yx⋅(1−f)P = \frac{y}{x} \cdot (1 - f)

Where $f$ is the trading fee rate (typically 0.5%).

The system also implements slippage optimization algorithms, reducing price impact of large trades through dynamic liquidity allocation. Optimized slippage calculation is as follows:

S=1−k(x+Δx)⋅(y−Δy⋅(1−f))S = 1 - \frac{k}{(x + \Delta x) \cdot (y - \Delta y \cdot (1 - f))}

Threshold Signature Security Architecture

PizzaFun employs Threshold Signature Scheme (TSS) as its security foundation, a distributed signature mechanism requiring cooperation of at least t participants (out of n total, where t≤n) to generate valid signatures. Formally expressed as:

TSS(t,n)→sig  ⟺  ∣Participants∣≥t\text{TSS}(t, n) \rightarrow \text{sig} \iff |\text{Participants}| \geq t

The system implements a combination scheme of Shamir Secret Sharing and Elliptic Curve Cryptography (ECC), distributing private keys across different nodes. The specific implementation employs an optimized ECDSA-TSS protocol, represented through the following process:

  1. Key Generation: Each participant $P_i$ generates secret share $s_i$, satisfying $s = \sum_{i=1}^n s_i$, where $s$ is the final private key

  2. Pre-signature Phase: Participants exchange Paillier-encrypted intermediate values

  3. Signature Generation: At least t participants collaborate to generate the final signature without reconstructing the complete private key

This architecture provides security levels comparable to cold wallets while maintaining efficient transaction processing. Theoretical security analysis shows that assuming at least $(n-t+1)$ honest nodes, attackers cannot crack private keys or forge signatures, even with complete control of $(t-1)$ nodes.

Zero Gas Fee Implementation Mechanism

PizzaFun achieves breakthrough zero gas fee transactions through an innovative resource allocation model that solves on-chain congestion issues. This mechanism is based on the following core technologies:

  1. Transaction Classification and Priority Queues: The system categorizes transactions into different priorities, using Weighted Fair Queuing (WFQ) algorithms for scheduling

  2. Batch Processing Optimization: Transactions are bundled for execution through batch processing mechanisms, sharing fixed costs. Batch processing efficiency function:

    Eb=Ci∑i=1nCi⋅(1−Ovn)E_b = \frac{C_i}{\sum_{i=1}^n C_i} \cdot (1 - \frac{O_v}{n})

    Where $C_i$ is individual transaction cost, $O_v$ is validation overhead, $n$ is batch size

  3. Validation Resource Pool: The platform maintains dedicated validator node pools, funded by approximately 15% of revenue

  4. Anti-abuse Mechanisms: Implements reputation-based rate limiting, where user transaction frequency limit $F_{max}$ is determined by:

    Fmax(u)=Fbase+min⁡(Ru⋅α,Fcap)F_{max}(u) = F_{base} + \min(R_u \cdot \alpha, F_{cap})

    Where $R_u$ is user reputation score, $\alpha$ is amplification factor, $F_{base}$ is base frequency, $F_{cap}$ is the upper limit

This zero gas fee model enables PizzaFun to provide frictionless trading experiences for users while maintaining system sustainability through economic design.

CrustNet Network Topology

PizzaFun employs a hierarchical network topology, optimizing inter-node communication efficiency and fault tolerance:

               ┌─────────┐
        ┌──────│ Core Layer  │──────┐
        │      └─────────┘      │
        ▼                       ▼
   ┌─────────┐             ┌─────────┐
┌──│Distribution Layer│◄───────────►│Distribution Layer│──┐
│  └─────────┘             └─────────┘  │
▼                                       ▼
┌─────────┐                         ┌─────────┐
│Access Layer│◄───────────────────────►│Access Layer│
└─────────┘                         └─────────┘

The network hierarchy includes:

  • Core Layer: High-performance validator nodes responsible for consensus formation and final state maintenance

  • Distribution Layer: Relay nodes responsible for message routing and data synchronization

  • Access Layer: User-facing edge nodes handling transaction submission and queries

Connectivity between nodes is determined by optimization formulas:

Copt=log⁡(n)+β⋅log⁡(1/ϵ)log⁡(log⁡(n))C_{opt} = \log(n) + \frac{\beta \cdot \log(1/\epsilon)}{\log(\log(n))}

Where $n$ is network scale, $\epsilon$ is expected failure rate, $\beta$ is system security parameter.

This topology ensures high availability and data consistency even under large-scale network attack scenarios.

Transaction Acceleration Algorithm

PizzaFun implements an innovative transaction acceleration algorithm—Velocity Boost—improving transaction response speed through predictive execution and speculative validation. The algorithm's core is Transaction Dependency Graph (TDG) analysis, used to identify potential transaction dependencies:

Gtdg=(V,E)G_{tdg} = (V, E)

Where $V$ is the transaction set and $E$ represents inter-transaction dependencies.

The system utilizes machine learning models to predict transaction paths, further optimizing execution order. Prediction accuracy can be expressed as:

Apred=TP+TNTP+TN+FP+FNA_{pred} = \frac{TP + TN}{TP + TN + FP + FN}

Where TP (True Positive), TN (True Negative), FP (False Positive), and FN (False Negative) are classification statistics of prediction results.

In practical applications, this algorithm optimizes transaction confirmation time from an average of 2 seconds to 92% of transactions completing confirmation within 1.2 seconds, greatly improving user experience.

Scalability Design

PizzaFun employs horizontal scaling architecture, supporting smooth system expansion as users and transaction volumes grow. Core scaling strategies include:

  1. Dynamic Sharding: The system automatically adjusts shard number and size based on load, with shard count determined by:

    Sopt=⌈T⋅CtPn⋅Ef⋅(1−Oc)⌉S_{opt} = \lceil \frac{T \cdot C_t}{P_n \cdot E_f \cdot (1 - O_c)} \rceil

    Where $T$ is expected transaction volume, $C_t$ is per-transaction cost, $P_n$ is per-node processing capacity, $E_f$ is parallel efficiency, $O_c$ is coordination overhead

  2. State Channels: For frequently interacting users, the system supports off-chain state channels, submitting only final states when channels close

  3. Cross-shard Transaction Protocol: Employs two-phase commit protocols to handle cross-shard transactions, ensuring atomicity

  4. Adaptive Resource Management: The system dynamically allocates computing resources based on historical data and predictive models

This scaling architecture enables PizzaFun to theoretically support concurrent transactions for hundreds of millions of users globally while maintaining low latency and high security.

System Security and Privacy Protection

Beyond the core TSS security architecture, PizzaFun implements multi-layered security protection measures:

  1. Formal Verification: Critical protocols and algorithms undergo formal verification through Coq proof assistants, ensuring mathematical correctness

  2. Zero-Knowledge Proofs: Transaction validation employs zk-SNARKs technology, proving transaction validity without revealing transaction details

  3. Hardware Security Module (HSM) Integration: Core nodes utilize physical HSMs for additional security protection

  4. Dynamic Intrusion Detection: The system monitors abnormal transaction patterns, assessing potential threats through risk scoring models:

    Rscore=∑i=1kwi⋅fi(x)R_{score} = \sum_{i=1}^k w_i \cdot f_i(x)

    Where $f_i$ are evaluation functions for different risk factors and $w_i$ are corresponding weights

  5. Secure Coding Practices: The codebase follows OWASP security standards, regularly undergoing static analysis and dynamic fuzzing tests

These measures collectively form a comprehensive security framework, providing the highest level of protection for user assets.

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