Thermal: eligibility repair

Review the independently proposed patch below, including its unchanged callers. Work in the real product frontend and the transactional backend. Integrate only the positive area of linearly interpolated temperature above threshold, including crossings inside sample intervals. All carriers need certification when requested. The UI accepts transit duration, while the API accepts exclusive end time. Charge ceiling transit hours and count confirmed transit minutes only. An eligibility regression changes which plans are accepted. Repair the domain rule and preserve persistence, capacity checks and error handling. Run bash test/run.sh. The public checks drive Chromium against native HTTP and a real database; each scoring group includes regression safeguards.

Review focus: full-stack-product