ROCQ Proofs

This publication collects three ROCQ-based verification studies developed within the Campbell Framework research program. The papers examine formal state-transition validation in Constraint Triangulation Theory, machine-auditable coherence verification of Titan lattice architectures, and simulation-based analysis of adaptive behavior across biological cytoskeletons, trinary computational lattices, and Titan material systems. Together, these works explore whether complex systems can be represented through bounded constraint relationships, quantified coherence metrics, and formally verifiable state architectures. The collection demonstrates the use of theorem-proving methods, lattice validation frameworks, and cross-domain simulation to investigate stability, regeneration, and survivability in engineered, computational, and biological systems. The results establish formal consistency of the encoded models and provide a foundation for future experimental validation, materials testing, and computational implementation. These studies are intended as verification and hypothesis-generation research rather than claims of empirical proof.