Unified Layer-0 Infrastructure for Post-Quantum Distributed Computing via High-Dimensional Mersenne Lattices

Abstract

This paper proposes a unified Layer-0 infrastructure protocol for post-quantum distributed computing, based on high-dimensional coordinate representations derived from non-commensurate Mersenne primes. Unlike traditional approaches reliant on block-based ledgers or persistent state replication, the proposed Mersenne Lattice Protocol (MLP) represents data, transactions, and authority states as coordinates within a high-dimensional lattice space. By projecting computational events into a 4096-dimensional vector space, MLP enables theoretically unbounded parallel transaction processing under resonance-based validation, while simultaneously eliminating permanent state storage at the protocol level. Furthermore, the protocol integrates Heart Rate Variability (HRV) as a dynamic physiological entropy source for stateless bio-key regeneration, thereby binding cryptographic authority to real-time biological liveness and spatiotemporal context. Functional prototypes of the core MLP architecture have been implemented and verified through a live demo environment (https://www.icekey.cloud/teleport_v), demonstrating peak throughput exceeding 45,000,000 TPS in a parallel resonance cluster. This framework provides the foundation for post-quantum secure financial systems, stateless media reconstruction, critical infrastructure protection, and delay-tolerant interplanetary communication.