Data plane verification (DPV) is important for finding network errors. Current DPV tools employ a centralized architecture, where a server collects the data planes of all devices and verifies them. Despite substantial efforts on accelerating DPV, this centralized architecture is inherently unscalable. In this paper, to tackle the scalability challenge of DPV, we circumvent the scalability bottleneck of centralized design and design Coral, a distributed, on-device DPV framework.The key insight of Coral is that DPV can be transformed into a counting problem on a directed acyclic graph, which can be naturally decomposed into lightweight tasks executed at network devices, enabling scalability. Coral consists of (1) a declarative requirement specification language, (2) a planner that employs a novel data structure DVNet to systematically decompose global verification into on-device counting tasks, and (3) a distributed verification (DV) protocol that specifies how on-device verifiers communicate task results efficiently to collaboratively verify the requirements. We implement a prototype of Coral. Extensive experiments with real-world datasets (WAN/LAN/DC) show that Coral consistently achieves scalable DPV under various networks and DPV scenarios, i.e., up to 1250× speed up in the scenario of burst update, and up to 202× speed up on 80% quantile of incremental verification, than state-of-the-art DPV tools, with little overhead on commodity network devices.