A Graduated Pair-Symbol Numerical Encoding Framework for ROM Optimization and High-Throughput Network Transmission

The Graduated Numerical Encoding System (GNES) is a mathematical and engineering architecture designed to compress and transmit high-precision numerical data (down to 10^{-12} precision) using a fixed 4-byte (32-bit) representation reduced to a compact Quad-Byte Hexadecimal payload (e.g., 0xF43DFC3D). Key Highlights & Benefits Zero-Loss Reversibility: Mathematically proven lossless recovery with zero residual error, verified through an automated $1,000,000$-sample stress test. ROM Hardware Optimization: Cuts silicon area and reduces dynamic power consumption by 46.5% using a 16-LUT Verilog hardware decoder with a 1.12\text{ ns}$ propagation delay. Network Transmission Acceleration: Decreases numerical payload size by 50% to 71.4%, significantly optimizing bandwidth usage and router processing speeds across 5G/6G networks.