PeoChain introduces a revolutionary blockchain architecture that mathematically solves the blockchain trilemma through the innovative Proof of Synergy (PoSyg) consensus mechanism. This paper presents a comprehensive solution that achieves scalability exceeding 100,000 transactions per second, maintains true decentralization with over 10,000 validators, and provides cryptographic security guarantees through formal verification. The architecture incorporates Subnet Validator Networks for parallel transaction processing, Dynamic Contribution Scoring for Sybil resistance, and algorithmic price stabilization mechanisms for economic stability. Mathematical analysis demonstrates Nash equilibrium properties of the consensus mechanism, while empirical evaluation on a global testnet validates theoretical predictions. PeoChain's integration of mobile financial services at the protocol level addresses the financial inclusion needs of 1.4 billion unbanked individuals globally. The system maintains transaction costs below $0.04 with subsecond finality, enabling micropayments and cross-border remittances at unprecedented efficiency. Formal verification using TLA+ specifications provides mathematical proofs of safety and liveness properties under Byzantine failure conditions.