Discrete Kakeya cover for LLM KV cache: D4/E8 nested-lattice quantisation realising a Kakeya-style tube-cover over the direction sphere. 2.4x-2.8x compression at <1% perplexity loss on Qwen3, Llama-3, DeepSeek, GLM-4, Gemma. Drop-in transformers.DynamicCache. pip install kakeyalattice.