Modern artificial intelligence is fundamentally constrained by the von Neumann bottleneck, dedicating vast energy and latency to shuttling data between RAM and processing cores to execute dense matrix multiplications. This paper proposes a Compute-in-Memory (CiM) architecture based on a discrete four-dimensional rhombohedral (D4) adjacency graph, bypassing traditional tensor operations entirely. By unifying compute and memory into a single, localized logic block that communicates exclusively with 24 hardwired neighbors, information processing emerges natively through structural geometric equilibration rather than algorithmic execution. We provide the exact mathematical translation of this topological framework into discrete digital logic, define the foundational D4 Logic Element (LE), and establish quantitative baselines for performance. Finally, we propose a rigorous FPGA bench test to empirically validate the predicted 103 to 104 magnitude improvements in latency and energy efficiency over standard GPU-based AI architectures.