Exact Ω₂ Identities for S₄,₂(x) with Performance Gains

We present exact closed-form identities for the weight-6 Euler sum S₄,₂(x) = Σ(n≥1) Hₙ₋₁x^n/n^5 at three rational points x ∈ {1/2, 1/4, -1/2}, expressed as rational linear combinations of a canonical 21-element Ω₂ basis. Coefficients were discovered via PSLQ with residuals <10^-96. Our software implementation demonstrates amortized performance gains through constant-folding optimization. Benchmarks show 12-21× per-evaluation speedup over direct series summation at 120 decimal digits (CPU), and 9000× throughput improvement for batched evaluation (GPU). Complete reproducible Python package with all exact coefficients available at:https://github.com/keewillidevnet/S42-omega2-reproducibility