Local Stability Does Not Imply Cross-Family Comparability: A Minimal Interface-Family Stress Test

This technical note presents a minimal synthetic stress test on the relation between local stability, cross-family comparability, and oriented arbitration. The study introduces a controlled interface-family toy model in which a locally stable witness is generated within a native family and then evaluated against multiple target families. The analysis distinguishes target-family fit, burden shift, target overlap, shared currency, persistent comparability, and oriented arbitration value. The main synthetic result is negative and methodological: high local stability within a family does not imply global comparability across families, and high fit does not imply high arbitration. In particular, the stress test identifies global-fitting non-discriminating regimes, where a target family absorbs or fits the witness well while exhibiting low arbitration value. Threshold-sensitivity and formula-sensitivity checks are included to test the robustness of the qualitative separation. A small frozen real-data sanity check on a tabular benchmark is also reported as a secondary, non-generalizing control. The note does not propose a general theory of arbitration, introduce new physical models, or make ontological claims. Its purpose is diagnostic: to provide a reproducible toy model for separating local stability, fit, comparability, and cross-family arbitration in controlled settings.