Aegis is a distributed computing framework that integrates Byzantine fault-tolerant consensus, secure multiparty aggregation, differential privacy, and blockchain-based auditability into a unified architecture. The system is designed to achieve trust, privacy, and verifiability without relying on central authorities. The framework introduces Local Audit Chains, which allow every node to maintain a verifiable log of its operations while preserving privacy. A hybrid consensus protocol combines stake and reputation mechanisms with adaptive timeouts to ensure safety and liveness under partial synchrony. Differential privacy is applied at the data aggregation layer using adaptive budgeting and Laplace or Gaussian noise mechanisms. Formal verification using the Z3 solver is used to prove core safety and liveness properties. Experiments demonstrate sub-second consensus latency and high audit integrity across a network of distributed nodes. Aegis provides a foundation for secure, privacy-preserving, and self-auditing distributed systems suitable for modern decentralized infrastructure.