The unprecedented growth of foundation models and edge computing has exposed the structural limitations of the von Neumann architecture, specifically the physical constraints of storage and network bandwidth. Current compression algorithms are universally bound by Shannon's channel capacity limits when attempting to process exabyte-scale data natively. This paper introduces a paradigm-shifting 'Zero-Storage' distributed computing architecture that circumvents the mathematical Inverse Problem. Instead of transmitting physical payloads, the proposed system employs a high-dimensional Mersenne Prime Universal Lattice Engine synchronized across both sender and receiver nodes. By executing deterministic inverse mapping, massive data arrays (e.g., 50GB neural networks) are pinpoint-mapped onto specific phase vectors within a 4096-dimensional space, yielding a singular coordinate seed of less than 256 bytes. This seed is fused with quantum entanglement noise and spatiotemporal entropy for post-quantum cryptographic security. Upon transmission, the source data undergoes stateless vaporization. To validate this architecture, a live prototype system was successfully implemented, demonstrating the immediate stateless vaporization of cryptographic keys and reversible data mapping entirely within volatile browser memory environments without physical storage dependencies. The receiving node materializes the original structure flawlessly on volatile memory (RAM) utilizing parallel processing expansion, entirely bypassing physical non-volatile storage (SSD/HDD) I/O. This zero-storage methodology presents a net-zero latency and power-efficient solution for extreme networking environments, including space data centers and tactical edge networks.