Line-Rate Spine-Leaf Network Coding: 80 Gbps on a Single Commodity CPU Core

We present a complete, Hardware-Sovereign network coding pipeline for spine-leaf datacenter fabrics, translating Tutte's nowhere-zero flow theory over GF(5) into a carrier-grade, line-rate routing protocol. Using a production SGP topology (4 spines, 8 leaves), we construct an explicit GF(5) nowhere-zero flow via Gaussian elimination over the signed incidence matrix. We formally establish the network's resilience, constructively proving tolerance to two simultaneous spine failures (N-2), bounded precisely by the structural collapse of the Betti number. Furthermore, we demonstrate exact three-source simultaneous network coding, decodable across any three surviving spines, and identify a strict structural ceiling at four sources under simple broadcast relay. Crucially, we shatter the performance limitations of traditional software-defined routing. By implementing a branchless, magic-multiply modular reduction scheme in ARM NEON and x86 AVX2 intrinsics, our decoding kernel achieves sustained throughput exceeding 80 Gbps on a single consumer-grade ARM Cortex-X3 core. Evaluated across 16,000,000 test packets in multiple failure topologies and execution environments (ARM physical device, x86 container, x86 cloud sandbox), the decoder yielded zero mismatches. This result demonstrates that resilient, multi-source network coding can operate at near-100GbE line rates entirely on commodity silicon, eliminating the CAPEX dependency on dedicated SmartNICs or FPGAs. While this work does not attempt to resolve Tutte's open 5-flow conjecture, it successfully weaponizes its algebraic properties into a deployable, rigorously hardware-verified infrastructure technology.