Operational trace adequacy for the double-tank closed-loop model

Prove that every coherent trace generated by repeated plant evolution, sampling, and controller execution for admissible double-tank parameters satisfies the quantitative predicate `is_closed_loop_trace`, thereby establishing the operational-to-trace bridge required for end-to-end assurance of no-overflow safety, bounded settling, stable tracking, and availability.

Background

The R10 reconstruction proves the four double-tank requirements from an explicit quantitative trace contract represented by is_closed_loop_trace. However, the operational theories describe repeated plant, sampling, and controller execution separately, and the paper does not establish that every coherent trace produced by those operational components satisfies the trace-contract predicate.

This unresolved semantic bridge is designated DT-R011. Its intended theorem assumes admissible parameters and an operational closed-loop trace, and must show that the trace satisfies is_closed_loop_trace. Establishing it would connect the operational execution layer to the R10 quantitative assurance results and complete the end-to-end verification argument.