We present W1H-SPQ, a binary hashing architecture for approximate nearest neighbor search that exhibits no upper dimensional limit. The method partitions embedding vectors into 24-dimensional slices and constructs a Weighted 1-Hodge Line Graph per slice, extracting two orthogonal spectral witnesses via power iteration and Hotelling deflation. Each slice contributes an independent binary discriminator; by the Chernoff-Hoeffding bound, error probability decays exponentially with the number of slices, inverting the curse of dimensionality observed in all prior ANN methods. Empirical validation on ARM Cortex-X3 (Snapdragon 8 Gen 2, no GPU) demonstrates a phase transition at D=8,192: W1H-SPQ achieves 100% Recall@50 from D=8,192 through D=65,536, while FAISS IVF-PQ degrades from 43% to 7% at identical memory budget (32 bytes/vector). On real text embeddings (20 Newsgroups, D=768), W1H-SPQ achieves 96% Recall@50 with no training data. Index construction scales linearly O(D). Memory compression reaches 128x over flat float32 storage at D=65,536. No upper dimensional limit has been identified through D=131,072.
Andrés Sebastián Pirolo (Thu,) studied this question.