A Catastrophe-Theoretic Framework for Regime-Switch Losses: Diagnostic Indices Are Not Welfare Criteria

Crisis diagnostics quantify geometric proximity to regime change, but their normative status is often overstated. Objective: To determine when catastrophe-based diagnostic indices can legitimately acquire normative content in welfare analysis. Method: The paper develops a dynamic governance model with deformable triple-well potential geometry, catastrophe-theoretic discriminants, and planner objectives under baseline and reform channels. Results: Diagnostic minimization and welfare maximization are shown to be non-implicative in general; under an explicit reform channel and an internalized switching-loss term, local reductions in HCFI become directionally aligned with welfare improvement. A stylized Soviet-Russia path and a reproducible computational protocol illustrate the mechanism. Conclusions: Catastrophe-based diagnostics are not welfare criteria per se, but they can acquire normative relevance when structural deformation and switching exposure are explicitly incorporated into the policy objective.