Emerging distributed computing architectures, such as grid and cloud computing, depend on the high integrity execution of each system in the computation. While integrity measurement enables systems to generate proofs of their integrity to remote parties, we find that current integrity measurement approaches are insufficient to prove runtime integrity for systems in these architectures. Integrity measurement approaches that are flexible enough have an incomplete view of runtime integrity, possibly leading to false integrity claims, and approaches that provide comprehensive integrity do so only for computing environments that are too restrictive. In this paper, we propose an architecture for building comprehensive runtime integrity proofs for general purpose systems in distributed computing architectures. In this architecture, we strive for classical integrity, using an approximation of the Clark-Wilson integrity model as our target. Key to building such integrity proofs is a carefully crafted host system whose long-term integrity can be justified easily using current techniques and a new component, called a VM verifier, which comprehensively enforces our integrity target on VMs. We have built a prototype based on the Xen virtual machine system for SELinux VMs, and find that distributed compilation can be implemented, providing accurate proofs of our integrity target with less than 4% overhead.