Winnex AI: Corrected O(K) Riemannian HMC Benchmark — Validation of Enterprise-Grade Inference Stack

Validated Mathematical Proof with Executable Kaggle Benchmark Abstract This record provides the independently verified, fully reproducible benchmark for the Winnex AI enterprise inference stack, correcting six critical implementation bugs identified in the original public benchmark (Zenodo 19630736). The system integrates Hamiltonian Monte Carlo (HMC) Riemannian navigation on S^(d-1), Johnson-Lindenstrauss (QJL) dimensionality compression (384D to 128D), and Quaternionic Spectral Attention (PsiQRH H4+M10) to achieve topology-preserving semantic retrieval. Corrections Applied QJL matrix projection (not slicing): Proper Johnson-Lindenstrauss random matrix preserves pairwise distances with epsilon=0.071 distortion SO(4) quaternion training: Commutativity weight cw=0.9746 after corpus training (vs identity in original) All 4 quaternion components used in similarity computation (not 2 of 4) H4 gate modulates HMC navigation scores instead of overwriting them Hanning window applied in time domain before FFT (not frequency domain) Navigation complexity O(K) over K=8 anchors, independent of corpus size N Benchmark Results Ablation: flp_bad=0 across all 6 gap levels; Spearman rho gain +0.0761 Scalability: Navigation time sub-linear from 10 to 10,000 chunks (39ms to 653ms) Real data: NDCG@10 technical tie vs FAISS exact search (0.02623 vs 0.03005) despite operating on 3x compressed vectors Enterprise Stack The full Winnex AI microservice stack (22 containers, 154 scripts, 56K+ LOC) is deployed on production infrastructure with Redis, pgVector, and GPU-accelerated SGLang inference, validating hardware accessibility on commercial server hardware (NVIDIA RTX 5060 Ti 16GB). Complete executable benchmarks available on Kaggle with GPU P100. License: Business Source License 1.1 (same as Zenodo 19630736).