Physical-layer network codes for consensus-testing (CT) via a relay are proposed, where each of two parties knows a message and can find out if all messages are equal, e.g. as an integrity check in a decentralized storage system or the control of mobile autonomous robots. By assumption, the encoders cannot randomize. The proposed codes achieve the CT capacity for channels with a memoryless uplink multiple-access channel that is a binary adder channel or a pair of q-ary symmetric or erasure channels. There, the capacity of noiseless uplinks can always be achieved, by using generalized deterministic identification (ID) codes for the uplink, testing consensus at the relay, and broadcasting the one-bit result using zero rate. For pairs of Gaussian channels and Gaussian adder channels, the capacity bounds equal those known for ID over certain noiseless uplinks, where the code sizes scale superexponentially in the block length. Using a recent derandomization result for decoders, it is shown that for general channels, the ID capacity of certain noiseless uplinks upper-bounds the CT capacity. In contrast, both for transmission coding for the uplink and additive linear network codes, the asymptotically achievable code sizes and necessary block lengths are shown to be suboptimal.