Per-input-channel rescale s_i = H_ii^alpha (identity-preserving via W<-Ws, H<-H/s/s) should compose with FWHT Gaussianization — channel equalization makes the post-rotation tile distribution closer to white iid Gaussian
Parabola minimum at alpha~0.15 ± 0.025. Default alpha=0.5 (SmoothQuant paper) is wrong for this pipeline. KLD pending.
NEW 3-BIT WINNER at α=0.20. Bracket cell (added 2026-04-08) showed α=0.20 beats α=0.25 by -0.230 PPL — the parabola minimum sits left of where the original {0.15, 0.25, 0.50} grid suggested. Clean V-shape on {0.00, 0.15, 0.20, 0.25, 0.50}. Total 3-bit gain over α=0 is now -1.867 PPL (vs -1.637 before), still ~6x the 4-bit α gain. 3-bit canonical recipe = gptq_turbo_e8_q3 + α=0.20 + k_proj@Q8_0 @ 21.6478 PPL @ 3.396 bpe. Worth a tighter bracket at α=0.18 / 0.22 to confirm 0.20 isn't a coarse-grid artifact. KLD pending.