Miden redefines the essence of trading — no longer just a public replay on the network, but a combination of local state transitions with cryptographic proofs. Accounts execute code on the client side, independently update their own state, and can generate or consume proofs (notes) of off-chain assets or messages. This design allows users to perform computations locally, with the network only needing to verify the validity of proofs without re-executing. Architecturally, accounts have full computational autonomy, and assets and messages circulate off-chain through proofs, with final confirmation occurring at the network layer. This approach significantly reduces on-chain computational load while maintaining consistency and security of the state.