PoAT Mathematical Model

General Definition

Each node n_i in the network is assigned a Dynamic Trust Index (T_i), calculated by AI according to the formula:

T_i = (0.4 _ S_i) + (0.3 _ R_i) + (0.2 _ A_i) + (0.1 _ P_i)

Where:

• S_i (Stake): the node's stake value, reflecting the level of financial commitment.
• R_i (Reputation): the reputation score calculated by AI based on historical behavior.
• A_i (Accuracy): the accuracy of transaction confirmations in one cycle.
• P_i (Performance): the node's performance index, measured by throughput (TPS) and latency.

Validator Selection Probability Function

Pr(V_i) = Tⁱ_a / Σ^N_j=1 T^a_j

With:

• a is the amplification factor adjusted by AI (0.8 ≤ a ≤ 1.2).
• N is the total number of active nodes.
• The probability is updated every 30 seconds based on the Reputation Forecasting LSTM model.

Consensus and Machine Learning Algorithm

Reinforcement Learning Algorithm

The central AI of PoAT is built on a Q-learning model, where the agent learns based on "consensus rewards":

Q(s, a) = Q(s, a) + ŋ [r + γ max_a' Q(s', a') - Q(s, a)]

Where:

• s: network state (number of active nodes, current TPS).
• a: action (change confirmation threshold, shard distribution, lock suspected node).
• r: reward – increases if the transaction is valid, decreases if there is an error or dispute.
• ŋ: learning rate.
• γ:discount factor for experience.

Over time, the AI self-optimizes to achieve:

• Maximum network performance (Throughput).
• Minimum validation latency (Latency < 500ms).
• Stable transaction error rate (Error Rate < 0.01%).

Multi-Layer Tracing Model

Tracing System Structure Tracing is implemented in a 5-functional layer architecture, ensuring integrity and independent auditing capability:

Data Integrity Mechanism Each transaction has an independent trace record with the structure:

TraceRecord = {trace_id, tx_hash,timestamp, validator_id, ai_risk_score,signature}

• trace_id:unique identifier.
• ai_risk_score: AI risk score (0.0 - 1.0).
• signature: ECDSA digital signature verified by node.

The root of the TraceRecord set is included in the header block, ensuring that every query is verifiable via Merkle Proof.

Security architecture and active defense mechanisms

PoAT deploys a multi-layered security model (Defense in Depth):

1. Layer 1 – Network security: TLS 1.3 encryption, dynamic firewall, automatic DDoS attack detection system.
2. Layer 2 – Data security: AES-256 and SHA-512, combined with differential encryption (Differential Privacy).
3. Layer 3 – AI monitoring: AI detects 21 common types of network attacks, 99.7% accuracy.
4. Layer 4 – Tracing & Auditing: all actions are saved on Trace Ledger, can be reversed.
5. Layer 5 – Governance & Access Control: multi-level access authorization (RBAC + ABAC).

The “AI Guardian Mode” mechanism allows the system to automatically isolate suspected nodes, then switch to manual monitoring status when necessary.

Optimize performance with Dynamic Sharding

Dynamic Sharding is an automatic scaling algorithm based on AI Load Predictor, which reduces network load and optimizes costs.

Shard_Count = f(TPS_avg,Node_active, Latency_mean)

AI predicts the number of shards needed to maintain stable TPS. When the network load increases, the system automatically splits new shards; when the load decreases, shards are merged to save resources.

This reduces operating costs by up to 40% compared to PoS or DPoS networks.