As the dimensionality of modern learned representations increases to thousands of dimensions, the state-of-the-art Approximate Nearest Neighbor (ANN) indices exhibit severe limitations. Graph-based methods (e.g., HNSW) suffer from prohibitive memory consumption and routing degradation, while recent randomized quantization and learned rotation approaches (e.g., RaBitQ, OPQ) impose significant preprocessing overheads. We introduce CRISP, a novel framework designed for ANN search in very-high-dimensional spaces. Unlike rigid pipelines that apply expensive orthogonal rotations indiscriminately, CRISP employs a lightweight, correlation- aware adaptive strategy that redistributes variance only when necessary, effectively reducing the preprocessing complexity. We couple this adaptive mechanism with a cache-coherent Compressed Sparse Row (CSR) index structure. Furthermore, CRISP incorporates a multi-stage dual-mode query engine: a Guaranteed Mode that preserves rigorous theoretical lower bounds on recall, and an Optimized Mode that leverages rank-based weighted scoring and early termination to reduce query latency. Extensive evaluation on datasets of very high dimensionality (up to 4096) demonstrates that CRISP achieves state-of-the-art query throughput, low construction costs, and peak memory efficiency.