The core of Lagrange Labs lies in zero-knowledge proof technology, a cryptographic magic that validates the authenticity of information without revealing the details of the data. In simple terms, it's like an 'invisible cloak' that protects data privacy while ensuring the credibility of computation results. Lagrange Labs excels in this area, applying ZK technology to the intersection of blockchain and AI, and has launched a series of breathtaking products. The foremost among them is the ZK co-processor, a technology that can be described as Lagrange's 'trump card.' It allows complex computations to be performed off-chain, generating ZK proofs that, upon verification, submit results to the blockchain. This design not only significantly reduces the costs of on-chain computations but also achieves high parallelization and horizontal scalability through its innovative Reckle Trees technology. Whether it's complex calculations in decentralized finance (DeFi) or cross-chain data queries, the ZK co-processor handles them with ease, providing developers with a handy tool. Even more impressive is DeepProve, Lagrange's zkML (zero-knowledge machine learning) solution. It verifies the reasoning process of AI models through zero-knowledge proofs, ensuring the credibility and privacy of outputs. Imagine, in medical diagnosis, patient privacy data does not need to be exposed while validating the accuracy of AI diagnoses; in DeFi risk analysis, complex model calculations can also be efficiently verified on-chain. This technology, which excels both internally and externally, not only enhances the credibility of AI but also opens new frontiers for Web3 applications.