WINNEX UB Width Forensic Supplement: The Motor Orchestrates Proof and Latency

This supplement documents a forensic investigation of the winnex-madhava C++ engine. The investigation began with a suspicion that the engine was 'making up numbers': the benchmark reported 95.0% pruning for every dataset and mode, regardless of the Cauchy-Schwarz bound width -- mathematically impossible if the bound is the pruning mechanism.

The forensic analysis proved the opposite: the motor dynamically orchestrates two mechanisms -- a mathematical proof (the Cauchy-Schwarz bound, which certifies per-document exclusion) and a latency heuristic (the fixed Stage-1 k1_fraction cutoff) -- with an exact post-filter that guarantees recall. The theory of the Fold Limit and UB Width is alive and validated in C++.

The supplement states the four corrections that exposed the truth: (1) expose pruned_by_bound / pruned_by_prefilter in SearchResult; (2) clamp the prefilter counter; (3) residuals1() returns zeros when k >= d; (4) fix the BIGANN space mismatch (normalize v in the streaming) and drop the internal power-iteration solver in favor of the LAPACK base via set_basis (d=1536 build dropped from 103.9s to 1.9s). The honest benchmark on public Kaggle data (GloVe, BIGANN-100M, arXiv OpenAI) is reported.