Conclusion

The tensor-free comparison is

Its proof requires a unital closed local algebra and a sufficiently rich state class, but no spatial complement. Its causal application additionally requires complete localized devices whose support action is proved. The finite gauge example shows both why the theorem applies and why a regional restriction alone is not a complete device interface.

The constructed observable limits retain products, sector data, state–effect pairings, and matched actions on their stated classes. They do not turn a finite constrained graph into a relativistic field theory by a change of terminology.