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 includes a vast arrayof relativistic field theories proposed as extensions to General Relativity(GR) or the Standard Model. While these models are phenomenologicallyattractive, many suffer from fundamental mathematical pathologies thatrender them physically nonviable. This report executes a comprehensiveaudit of candidate relativistic field theories suitable for the Causality-Stability Tester (CST) framework. We scrutinize scalar-tensor exten-sions (Galileons, DHOST), vector-tensor architectures (Proca, Einstein-Aether), and edge-case theories (Ghost Condensate, 4D Einstein-Gauss-Bonnet, ModMax) to determine their perturbative viability in the Minkowskilimit. We identify a clear hierarchy of candidates, distinguishing betweentheories that pass the CST gates, those that serve as stress tests, andthose that fail due to fundamental obstructions