We introduce the Universal Constraint Engine (UCE), a system for generating emergent multi-state architectures from declarative constraint rules over conserved quantities. Unlike conventional neural network architectures that rely on learned weights, gradient descent, and massive training corpora, UCE derives computational behaviors -- including memory, logic, hysteresis, and oscillation -- directly from symbolic constraints without any training phase. The system comprises four layers: a Rule Definition Layer, a Constraint Solver Layer, an Emergent Behavior Engine, and an Embodiment Mapper for translating symbolic architectures into hardware implementations spanning FPGA, neuromorphic, spintronic, and quantum substrates. Worked examples demonstrate that minimal rule sets produce non-trivial emergent behaviors analogous to SR latches, biological oscillators, and write-gated memory cells. Patent pending: U.S. Provisional Application No. 64/036,854.