1. The problem is to develop an AI-based system for counterfeit product detection and vendor authenticity verification. 2. While this is a conceptual and technical problem rather than a math problem, we can model the risk score calculation mathematically. 3. Suppose the authenticity risk score $R$ is a weighted sum of features: product image analysis score $I$, textual description consistency score $T$, pricing pattern anomaly score $P$, and vendor behavior score $V$. 4. The formula can be expressed as: $$ R = w_1 I + w_2 T + w_3 P + w_4 V $$ where $w_1, w_2, w_3, w_4$ are weights assigned to each feature based on their importance. 5. Each score is normalized between 0 and 1, where higher values indicate higher risk. 6. The system uses machine learning models to compute each score from the respective data sources. 7. The final risk score $R$ helps classify products/vendors as genuine or counterfeit/fraudulent based on a threshold. This mathematical model guides the AI system's decision-making process.