Lagrange's zero-knowledge proof (ZK) technology is demonstrating its strong potential in multiple fields. Below are ten representative application cases where this technology has been implemented, showcasing its innovative applications in real-world scenarios.

1. AI-assisted medical diagnosis verification:
Lagrange has partnered with medical institutions to develop the DeepProve system, which is used to verify the output accuracy of AI models in medical image analysis. This system has been successfully applied in the early screening of breast cancer, ensuring the reliability and completeness of diagnostic results.

2. Cross-chain DeFi risk management:
In the field of decentralized finance (DeFi), Lagrange provides real-time data verification services for multi-chain platforms such as Ethereum and Solana. For example, lending platforms utilize Lagrange's technology to verify users' collateral ratios of cross-chain assets, effectively reducing liquidation risks.

3. Layer 2 Scaling Solutions:
Lagrange supports multiple Layer2 projects (such as Mantle) to generate batch transaction proofs, significantly improving transaction processing capabilities. It can handle over 2 million transactions daily while reducing Gas costs by 90%, greatly enhancing the scalability of the blockchain.

4. Autonomous Driving Safety Verification:
Automakers are using Lagrange's ZK proof technology to verify the decision-making logic of autonomous driving AI in extreme situations, ensuring that the algorithms meet stringent safety standards and providing important support for the development of autonomous driving technology.

5. NFT Copyright Protection:
Through cross-chain verification technology, Lagrange provides verifiable proof of creation history for NFT trading platforms, effectively combating forgery and enhancing the trustworthiness of the digital art market.

6. Supply Chain Financial Innovation:
Logistics companies have adopted the Lagrange network to verify the authenticity of global freight data, achieving second-level trade finance settlement. This technology has been practically applied in the rubber trade chain in Southeast Asia, significantly improving the efficiency of supply chain finance.

7. Military Simulation Optimization:
Lagrange's algorithm is used to optimize the simulation of explosive shock effects from warheads, improving the accuracy of ballistic design. This technology originates from AUTODYN numerical simulation, demonstrating the potential applications of ZK technology in highly classified military fields.

8. Personalized Recommendations with Privacy Protection:
E-commerce platforms utilize Lagrange's ZK co-processor to analyze user behavior data, providing personalized recommendations while ensuring that the original data is not leaked through proofs, balancing user experience and privacy protection.

9. Carbon Emission Data Verification:
In the carbon trading market, Lagrange provides ZK verification services for enterprise energy consumption data. Currently, it has covered 300 factories in Europe, significantly improving the efficiency of annual emission reduction audits and providing technical support for achieving carbon neutrality goals.

10. Cross-chain game asset interoperability:
The blockchain game "Illuvium" integrates the Lagrange protocol, achieving cross-chain verification of game assets between Ethereum and Immutable X, providing players with a seamless asset transfer experience and expanding the possibilities of blockchain gaming.

These application cases rely on Lagrange's ZK co-processor and a network composed of over 85 nodes. It is reported that its testnet has generated more than 11 million proofs, while the mainnet is expected to officially launch in the third quarter of 2025. Lagrange's technology is demonstrating transformative potential across multiple fields, paving the way for the widespread application of blockchain technology.