Winnex AI: Corrected O(K) Riemannian HMC Benchmark — NDCG Technical Tie Validation (v51-final)

Validated Mathematical Proof with Executable Kaggle Benchmark Results B1 Ablation: flp_bad=0 across all 6 gaps B2 O(K): 33ms (10 chunks) to 155ms (10,000 chunks) — sub-linear scaling B3 Jena Climate: NDCG@10 FlatIP=0.08886 vs HMC=0.08886 — exact technical tie (delta=0.00000) 6 Bugs Corrected QJL matrix (not slicing), SO(4) trained (cw=0.51), all 4 quaternion components, H4 gate modulates (not overwrites), Hanning in time domain, QJL used everywhere. Zero fallbacks. Klein-Gordon relativistic kinetic energy integrated. GPU P100, PyTorch 2.10, ~4 min runtime. BSL 1.1 license.