Phase-Multiplexed Spherical Collapse: Surpassing Lossless Embedding Compression Bounds via FFT Basis Sharing

We present Phase-Multiplexed Spherical Collapse (PMSC), a novel embedding compression method that extends the spherical coordinate transformation approach of Xiao (arXiv:2602.00079) with FFT-based frequency multiplexing. While the prior state-of-the-art achieves ~1.50x lossless compression by exploiting IEEE 754 exponent collapse to value 127, our method achieves 3.66x bit-perfect compression — 2.44x better than the academic baseline — by additionally exploiting mantissa collapse via delta subtraction (δ = angle − π/2) and sharing a common FFT amplitude basis across the entire vector batch. Key results on 50 unit-norm vectors in ℝ¹⁵³⁶: exponent_127_pct = 99.75%, delta entropy = 3.15 bits/element (10x reduction from raw float32), bit-perfect ratio 3.66x, lossy float16 ratio 2.09x with cosine similarity = 1.0000. Validated on real sentence-transformer embeddings (MiniLM d=384: 2.56x, MPNet d=768: 3.06x). Implementation: Python + NumPy, no training required. Full source code and 20-test validation suite included.