knowledge: rotation vs error correction summary

Author: AdaWorldAPI

.claude/knowledge/rotation_vs_error_correction.md

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+# Rotation vs Error Correction
+
+## Core Finding (2026-03-26)
+
+Google TurboQuant (ICLR 2026) validates bgz17's design choices independently:
+
+- **Rotation before quantization**: TurboQuant uses Hadamard → Polar. bgz17 uses Euler-Gamma bundle rotation (Fujifilm X-Sensor). Same effect (overhead-free distribution equalization), different mechanism (geometry vs number theory).
+
+- **No error correction needed**: TurboQuant requires QJL (1-bit sign correction) because uniform quantization creates boundary bias. bgz17 does NOT need this because Fibonacci codebook entries sit at 1/4σ discrete positions with 3σ inter-qualia separation (99.73% assignment accuracy).
+
+- **No POPCOUNT needed**: Fibonacci encoding makes bits non-uniform (bit 4 = 8× bit 0). Hamming distance (POPCOUNT) would be wrong. Table lookup (`vpshufb`/`vtbl`) is both correct AND faster, and runs on any CPU since 2013.
+
+## Key Implication for ndarray
+
+All bgz17 distance kernels use `vpshufb` (AVX2) or `vtbl` (NEON) table lookups.
+No VPOPCNTDQ (AVX-512 Ice Lake+) dependency. No FP arithmetic for distance.
+NPU-compatible: INT8 table lookup is the NPU's native operation.
+
+## Full Spec
+
+See `docs/ROTATION_VS_ERROR_CORRECTION.md`