Spike timing offers a combinatorial address space, suggesting that timing-based spiking inference can be executed as lookup and routing rather than as dense multiply--accumulate. Yet most neuromorphic and photonic systems still digitize events into timestamps, bins, or rates and then perform selection in clocked logic. We introduce Polychronous Wave Computing (PWC), a timing-native address-selection primitive that maps relative spike latencies directly to a discrete output route in the wave domain. Spike times are phase-encoded in a rotating frame and processed by a programmable multiport interferometer that evaluates K template correlations in parallel; a driven--dissipative winner-take-all stage then performs a physical argmax, emitting a one-hot output port. We derive the operating envelope imposed by phase wrapping and mutual coherence, and collapse timing jitter, static phase mismatch, and dephasing into a single effective phase-noise budget whose induced winner--runner-up margin predicts boundary-first failures and provides an intensity-only calibration target. Simulations show that nonlinear competition improves routing fidelity compared with noisy linear intensity readout, and that hardware-in-the-loop phase tuning rescues a temporal-order gate from 55.9% to 97.2% accuracy under strong static mismatch. PWC provides a fast routing coprocessor for LUT-style spiking networks and sparse top-1 gates (e.g., mixture-of-experts routing) across polaritonic, photonic, and oscillator platforms.