The 5-Bit Eisenstein-Norm CRT: A 96 Ops/Cycle Inference Engine for Binary Silicon

This document presents a reduced arithmetic representation for the Eisenstein-Norm CRT framework. By decreasing the lane width from 10 bits to 5 bits (3 mantissa bits and 2 exponent bits), the number of independent lanes per 64-bit word doubles from 6 to 12, achieving a peak throughput of 96 operations per cycle—twice that of the 10-bit baseline—while energy per multiply-accumulate operation drops by a factor of 6.3 relative to the 10-bit configuration.The representation preserves all structural properties of the original framework: the hexagonal lattice geometry (proven by the Loewner torus inequality), the Unique Factorization Domain (UFD) structure of the Eisenstein integers, the Chinese Remainder Theorem (CRT) isomorphism, and the exact residue accumulator for addition.The 5-bit configuration supports a dynamic range of 1 to 56 with a uniform worst-case relative error of 12.5%. Four spare bits in the 64-bit register provide a free global correction mechanism that extends the effective mantissa to 7 bits and reduces the worst-case error to 0.78%. The architecture operates at 480,000 times the Landauer limit—6.4 times closer to the thermodynamic floor than the 10-bit baseline.The document provides a complete architectural specification: lane format, arithmetic pipeline, precision analysis, energy breakdown, reduced accumulator design, and comparison with existing formats (INT4, FP4). The 5-bit configuration offers 50% more operations per cycle than INT4 or FP4, four times the dynamic range of INT4, nine times the dynamic range of FP4, and exact accumulation. The design space is presented as a continuum, allowing users to select the optimal configuration for their workload.This work is a direct extension of the original Eisenstein-Norm CRT framework and is intended as a complementary inference-optimised mode to the 10-bit general-purpose configuration.