Due to the diverse physical attributes of computing resources and tasks, developing effective mechanisms to facilitate task and resource matching in complex connected systems for value-oriented task completion has become increasingly challenging. To address the challenge, this paper proposes a networked physical computing system that integrates the physical attributes of computing resources and tasks as well as task-specific trust relationships among devices to enable value-driven task completion. Specifically, we propose a state-of-the-art hypergraph-aided trusted task-resource matching (TTR-matching) framework to achieve the envisioned physical computing. First, a task-specific trusted physical resource hypergraph is defined, which integrates task-specific trust, the physical attributes of resources, and task types. This enables accurate modeling of device collaboration dependencies under specific task types. Next, a task hypergraph is generated to associate the task initiator with the physical attributes of the corresponding tasks. Based on these two hypergraphs, a hypergraph matching algorithm is designed to facilitate task-specific trusted collaborator selection and accurate task-resource matching for value-maximizing task completion. Extensive experimental results demonstrate that the proposed TTR-matching framework outperforms comparison algorithms in identifying task-specific trustworthy collaborators and maximizing the average value of task completion.