COREY: A Prototype Study of Entropy-Guided Operator Fusion with Hadamard Reparameterization for Selective State Space Models

State Space Models (SSMs), represented by the Mamba family, provide linear-time sequence modeling and are attractive for long-context inference. Yet practical deployments remain memory-bandwidth limited because selective state updates are often decomposed into fragmented kernels with repeated intermediate tensor materialization. We present COREY, a prototype framework that combines memory-aware operator fusion with Hadamard-based feature reparameterization. Activation entropy, estimated with fixed-width histograms, is used as a runtime scheduling statistic to place fusion boundaries and choose tile sizes. To regularize heavy-tailed activations, we absorb normalized Hadamard transforms into linear projections, preserving functional equivalence while reducing peak-coordinate concentration. In a controlled prototype study over heavy-tailed SSM activations, COREY consistently reduces proxy latency, improves throughput, and lowers DRAM traffic relative to unfused and fixed-depth baselines. Low-bit results are reported only through a hand-crafted stability proxy and are intended as diagnostic evidence rather than checkpoint-level quality claims. Code repository: https://github.com/mabo1215/COREY_Transformer.git.