We present the architecture of a classical computing system that implements quantum-like reasoning through two key innovations: (1) signed-weight registers that enable destructive interference, allowing wrong hypotheses to be actively cancelled rather than merely diluted; and (2) a cross-domain interference bus that automatically discovers connections between uncertain quantities in different domains when they share mathematical structure. The architecture delays all commitment (collapse) until output is requested, maintaining possibilities in superposition throughout intermediate computation. A working prototype demonstrates convergence on correct answers in multi-domain reasoning tasks, including a simulation of theoretical physics framework discovery that independently converges on the same conclusions reached through human geometric intuition. The system runs on standard classical hardware with no quantum components. We describe the five-layer architecture, the key design decisions that differentiate it from existing probabilistic and quantum-simulation approaches, the open engineering problems, and the theoretical basis connecting the architecture to the physics of information processing.