Operational Viability and Consistency of Relativistic Field Theories in the Minkowski Limit: A Candidate Audit for the CST Framework

The landscape of modern theoretical physics is populated by a vast array of relativisticfield theories proposed as extensions to General Relativity (GR) or the Standard Model.While phenomenologically attractive, many of these models suffer from fundamental math-ematical pathologies that render them physically unviable. This report executes a compre-hensive audit of candidate relativistic field theories suitable for the Causality-StabilityTester (CST) framework. We scrutinize scalar-tensor extensions (Galileons, DHOST),vector-tensor architectures (Proca, Einstein-Aether), and edge-case theories (Ghost Conden-sate, 4D Einstein-Gauss-Bonnet) to determine their perturbative viability in the Minkowskilimit. We identify a clear hierarchy of candidates, distinguishing between theories that passthe CST gates, those that serve as stress tests, and those that fail due to fundamentalobstructions.