Embedding Compression via Spherical Coordinates

We present a compression method for unit-norm embeddings that achieves 1.5$\times$ compression, 25\% better than the best prior lossless method. The method exploits that spherical coordinates of high-dimensional unit vectors concentrate around $\pi/2$, causing IEEE 754 exponents to collapse to a single value and high-order mantissa bits to become predictable, enabling entropy coding of both. Reconstruction error is below 1e-7, under float32 machine epsilon. Evaluation across 26 configurations spanning text, image, and multi-vector embeddings confirms consistent improvement.