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Low duty cycle operation is critical to conserve energy in wireless sensor networks. Traditional wake-up scheduling approaches either require periodic synchronization messages or incur high packet delivery latency due to the lack of any synchronization. In this paper, we present the design of a new low duty-cycle MAC layer protocol called Convergent MAC (CMAC). CMAC avoids synchronization overhead while supporting low latency. By using zero communication when there is no traffic, CMAC allows operation at very low duty cycles. When carrying traffic, CMAC first uses any cast to wake up forwarding nodes, and then converges from route-suboptimal any cast with unsynchronized duty cycling to route-optimal unicast with synchronized scheduling. To validate our design and provide a usable module for the community, we implement CMAC in TinyOS and evaluate it on the Kansei testbed consisting of 105 XSM nodes. The results show that CMAC at 1% duty cycle significantly outperforms BMAC at 1% in terms of latency, throughput and energy efficiency. We also compare CMAC with other protocols using simulations. The results show for 1% duty cycle, CMAC exhibits similar throughput and latency as CSMA/CA using much less energy, and outperforms SMAC and GeRaF in all aspects.