A wide range of organisms features molecular machines, circadian clocks, which generate endogenous oscillations with ~24 h periodicity and thereby synchronize biological processes to diurnal environmental fluctuations. Recently, it has become clear that plants harbor more complex gene regulatory circuits within the core circadian clocks than other organisms, inspiring a fundamental question: are all these regulatory interactions between clock genes equally crucial for the establishment and maintenance of circadian rhythms? Our mechanistic simulation for Arabidopsis thaliana demonstrates that at least half of the total regulatory interactions must be present to express the circadian molecular profiles observed in wild-type plants. A set of those essential interactions is called herein a kernel of the circadian system. The kernel structure unbiasedly reveals four interlocked negative feedback loops contributing to circadian rhythms, and three feedback loops among them drive the autonomous oscillation itself. Strikingly, the kernel structure, as well as the whole clock circuitry, is overwhelmingly composed of inhibitory, rather than activating, interactions between genes. We found that this tendency underlies plant circadian molecular profiles which often exhibit sharply-shaped, cuspidate waveforms. Through the generation of these cuspidate profiles, inhibitory interactions may facilitate the global coordination of temporally-distant clock events that are markedly peaked at very specific times of day. Our systematic approach resulting in experimentally-testable predictions provides insights into a design principle of biological clockwork, with implications for synthetic biology. Sleep/wake cycles in animals exemplify daily biological rhythms driven by internal molecular clocks, circadian clocks, which are important for plant life as well. The plant circadian clock is highly complex, eluding our understanding of its design principle. Based on the computational simulation of Arabidopsis thaliana, we successfully identified a kernel of the plant circadian system, the critical genetic circuitry for clock function. The kernel integrates four major negative feedback loops that process molecular circadian oscillations. Surprisingly, the plant clock circuitry was found to be overwhelmingly composed of inhibitory, rather than activating, interactions among genes. This fact underlies plant circadian molecular profiles to often exhibit sharply-shaped, cuspidate waveforms, which indicate clock events that are markedly peaked at very specific times of day. Our work presents experimentally-testable predictions, with implications for synthetic biology.